Trombones have gone through more permutations than some people may realize. Not only has history seen soprano, alto, tenor, bass, contrabass, and valve trombones, but an intriguing permutation of the instrument, called the rear-facing or over-the-shoulder trombone, pops up frequently in pictures and occasionally in museum holdings; e.g., here. For a YouTube clip of someone playing such an instrument, see here. (I prefer rear-facing as a descriptive term, since over-the-shoulder does not distinguish from the standard trombone, which already has a rear bow of tubing that extends over the player's shoulder.)
The very earliest examples of this version of the instrument likely reflect the working-out of the shape of the trombone; the standard trombone evolved, after all, as a "bent" version of the original straight trumpet. The exact manner and shape of this bent tubing was almost certainly not immediately standardized, and it is highly likely that there was some experimentation along the way.
Beginning in the late 18th century, there was a more general trend among all brass instruments toward over-the-shoulder instruments (see Boston Brass Band example, below). Trombones were part of this trend, which is said to have been at least partially the result of the desire for better ensemble balance (i.e., these highly directional brass instruments became generally softer).
Historian David Guion categorizes over-the-shoulder trombones as "no more than a temporary vogue" (Guion, A History 66). I'm not sure I completely agree. It depends on how you define temporary, of course. There are nine images from pre-1800 alone. Even if you discount those nine early examples (and I fail to see why you should), you're still left with a long, steady stream of iconography after that: 64 additional images from 10 different countries spanning a full century. A full century. That is chronologically too long and too widespread to be considered a "temporary vogue."
I would probably characterize it something like this: Iconography suggests that the over-the-shoulder trombone, which can be seen in a handful of images before the 19th century, became relatively widespread in the 19th century. Use of the instrument does not appear to taper off until the end of that century. Although there is significant variety in iconography, many of the images originate in France, and a large number of them depict military usage.
For additional historical context and full citation of sources, see Trombone History Timeline.
c. 1405—Paris, France: A grotesque from the Hours of Charles the Noble plays what is perhaps a proto-rear-facing trombone. There is no slide, obviously, so it is not a true trombone, but the similarity in general shape is obvious and could be seen as an early experiment in the direction of rear-facing brass instruments (see below image; public domain) (RIdIM/RCMI Inventory No. 8, p. 21).
1503-1529—Spain: A painting by either Joan Gascó or Gabriel Guardi includes an angel-trombonist playing what appears to be a rear-facing instrument. The first detail, below, shows the rear-facing bell, partially obscured by the halo, circled in red. The second detail shows more of the image, providing a view of the other halos and the materials nearby. Finally, the third image is the full painting (public domain image) (Ballester; French National Library).
c. 1504—Perpignan, France: A painting on an organ shutter (since relocated to the wall opposite the organ) in the Perpignan Cathedral (Cathedral Basilica of Saint John the Baptist of Perpignan, or Basilique-Cathédrale de Saint-Jean-Baptiste de Perpignan) depicts musicians at the Feast of Herod, including a rear-facing or over-the-shoulder trombone. Although there are some improbable aspects of the trombone, including the shape of the slide and the general configuration of the tubing, it seems unlikely that the artist would have misjudged the actual direction of the bell (see below detail; public domain; special thanks to Jean-Jacques Herbin).
1570—Waiting for the Princely Guests, an image depicting wind musicians in a balcony atop a triumphal arch, shows trombone, trumpets, bombard, and positive organ, as they prepare to play for a prince’s arrival (see below image; public domain) (Carter, Renaissance 278; Nuremberg, Stadtbibliothek).
1578—Antwerp, Belgium: A set of masses by George de La Hele includes a print–an initial D in front of a group of cherub musicians–that features a rear-facing trombone being played by a cherub (also rear-facing) (see below image; public domain; Wangermée vol. 1 167).
c. 1615—Cislago, Italy: The Church of Santa Maria della Neve contains an anonymous frescoed lunette featuring several angel musicians, including a trombonist playing a rear-facing instrument (see below image; public domain) (Morandi; Farioli).
c. 1660—Pierre Paul Sevin’s drawing of a performance of a mass for 4 choirs includes what appears to be a group of 3 trombones. At least one of them is a rear-facing instrument; the other 2 pictured do not have clearly visible bells (see detail and full image below; public domain) (Marx, The Instrumentation of Handel's Early Italian Works).
1689—The Netherlands: An etching by Dutch engraver Romeyn de Hooghe titled L’Europe Allarmée pour le fils d’un Meunier includes what appears to be a rear-facing trombone (see upper-left of full image). The print is a satire against James II (see below detail and full image below; public domain).
Late 17th Century—Bologna, Italy: An angel holding what is possibly a rear-facing trombone sits atop the organ case/backdrop of the older of two organs in San Petronio (see below image; special thanks to Adrian King, photographer).
1732—Prague, Czech Republic: Upon restoration of the Strahov monastery, monk-artist Siard Nosecky paints a fresco on the refectory ceiling that includes what appear to be two rear-facing trombones along with two horns and a tromba marina (see detail and full image below; public domain).
1781-1854—Amsterdam, Netherlands: Military Music, a catchpenny print produced by Erve H. Rijnders, includes a rear-facing trombone (see below detail; public domain image) (Catchpenny Prints of the Dutch Royal Library).
c. 1795—France: Trombonist André Braun publishes his method book, Gamme et Méthode pour let Trombones, which includes a position chart showing a rear-facing trombone (Weiner, Braun; Weiner, Braun Revisited; Dudgeon 194).
c. 1800—Germany: A print of military musicians entitled Turkische Musick der K. Baierischen Grendier Garde, now held in the Germanisches Nationalmuseum, includes a rear-facing trombone (see below detail; public domain).
c. 1800—Frankfurt am Main, Germany: Philipp Jakob Döring publishes a sheet of cut-outs of military musicians that includes a rear-facing trombone (see below detail; public domain) (German National Museum).
1801-50—Munich, Germany: A print illustrating various musical instruments includes a rear-facing trombone (see below detail; public domain) (German National Museum, graphic collection).
1805—Netherlands: A watercolor labeled Batavian Republic (now the Netherlands) and dated 1805 features trombonist in military uniform playing a rear-facing instrument (see below image; public domain) (New York Public Library Digital Gallery).
1806—France: An image depicting several French military musicians includes a rear-facing trombone (see below center); also included is another now-obsolete instrument, the serpent (see below right) (public domain image, source: New York Public Library Digital Gallery).
1807-08—Germany: Christoph and Cornelius Suhr, in their book on military uniforms in Hamburg (Abbildung der uniformen aller in Hamburg), depict musicians from the Dutch military in Hamburg from the years 1807-08. Included is a musician with an awkwardly-rendered rear-facing trombone (see below image; public domain).
1810-40—Strasbourg, France: An image by artist Boersch Thiébaut (1782-1861) that is part of set of figurines executed between 1810 and 1850 features musicians of the 14th Regiment, including 2 rear-facing trombones (see below image; public domain) (Paris, musée de l’Armée).
c. 1815—Munich, Germany: Musik der Bürger-Garde der Haupt u. Residenz-Stadt München, a print by J.C. Hochwind, includes players of both traditional and rear-facing trombones (see detail and full image below; public domain) (Ryan 202).
c. 1820—France: An etching titled The French Garrison, probably set in Normandy, depicts a group of French soldiers mingling with villagers. A fiddler and a regiment trombonist with a rear-facing instrument provide music for dancing while standing on a makeshift stage (see top-right of below image; public domain) (Fromrich 24).
c. 1820—Paris, France: An anonymous illustration of a French military band includes two rear-facing trombones (see top row of below image; public domain) (Camus, Military Musicians).
1820—An engraving entitled Banda Militare includes 2 rear-facing trombones (see below detail; public domain) (Oberlin Conservatory Special Collections).
1820-39—Rotterdam, Netherlands: A catchpenny print by T.C. Hoffers and A. van Alphen depicting several different military instruments includes 2 rear-facing trombones, one of which has a dragon-head bell (a type of trombone often called a buccin) (see below detail; public domain; Catchpenny Prints of the Dutch Royal Library).
1821—Italy: A depiction of a carpenter and 3 musicians from the Italian grenadiers includes a musician with a rear-facing trombone (see below image; public domain) (Melegari 147).
1824—Belgium: A pen and ink drawing of a Belgian military trombonist depicts a player in full military regalia playing a rear-facing trombone (see below image; public domain) (New York Public Library Digital Gallery).
c. 1825—France: Pellerin, publisher of French popular prints, publishes an image titled Musique d’Infanterie Francaise, which includes a soldier with a rear-facing trombone (see below detail; public domain) (Paris, Museum of Civilization in Europe and the Mediterranean).
1825-1850—Strasbourg, France: The Wurtz and Pées family produces paper figurines of various military units. Among them are numerous military musicians, including several with rear-facing trombones (see below 4 images; public domain).
1826—Broek, Netherlands: March of the Cavalry, a “catchpenny” military print that features numerous musicians, includes a man playing a rear-facing trombone on horseback (see below detail; public domain).
1828—France: An image from the Vinkhuijzen collection of military uniforms includes a trombonist on horseback playing a rear-facing trombone (see below image; public domain) (New York Public Library Digital Gallery).
1828—Paris, France: Caricaturist J. J. Grandville depicts a country dance in his lithograph, Sundays of a Good [Middle-Class] Citizen. At the front-center of the orchestra is a rear-facing trombone (see below image; public domain) (Fromrich 29).
c. 1830—Vienna, Austria: K.k. Österreichischer Militair Leichen-Conduct, lithograph no. 8 from a series edited by Michael Tretsentsky, shows a military band that includes trombones. The configuration is somewhat unusual in that it includes both traditional and rear-facing trombones (see below image; public domain) (Pirker).
1830—Strasbourg, France: Sometime before this date, a print by Jacques Perlasca of a mounted chasseur band illustrates both a standard rear-facing trombone and a rear-facing buccin (see detail and full image below; public domain) (Ryan 23).
1831—Belgium: A lithograph titled Musiciens d’infanterie belge, or “Belgian infantry musicians,” portrays a military musician holding what appears to be a rear-facing trombone (see below image; public domain) (Bibliotheque royale Albert I; Wangermée vol. 2, 264).
1832—Belgium: A print by Belgian artist Jean-Baptiste Madou titled Officier Garde Civique Premier depicts an officer of the Belgian Civil Guard. Behind the officer stands a military musician who appears to be holding a rear-facing trombone (see below image; public domain) (New York Public Library Digital Gallery). For a similar image, see 1831 (above).
1834–Paris, France: In his trombone method book, Grande Méthode de trombone, Vobaron includes a graphic showing a rear-facing trombone from both sides (see below image; public domain).
1837—Paris, France: Jean-Georges Kastner, a French composer and theorist, writes his orchestration treatise, Traité Général d’Instrumentation. The treatise includes a rear-facing valve trombone with a fingering chart (see below image; public domain).
1837—Johann Baptist Lachmüller’s print, Bamberg Maskerede, features 2 different rear-facing trombones (see below image; public domain). Special thanks to Tassos Dimitriadis.
c. 1839—Fribourg, Switzerland: Musica militaris, a print depicting musicians of the boarding school of Fribourg, features a percussionist and a trombonist with a rear-facing bell (see below image; public domain) (Bovet and Curchod 28).
1845—Rio de Janeiro, Brazil: Lithography firm Ludwig & Briggs publishes a print called Begging for the Holy Ghost, which includes a man playing a rear-facing trombone (see below image; public domain) (source: Google Arts & Culture, “Musica Brasilis”).
1845—Prague, Czech Republic: A drawing satirizing the Prague music conservatory (Satira na prazské hudební konzervativce) includes at least one rear-facing trombone (see upper-left of below image), and probably two (see upper-right) (public domain image) (Volek, pl. 315).
1847—Paris, France: An article in the periodical L’Illustration titled “Le Pupitre de Palestrina” (“The Desk of Palestrina”) is accompanied by an image by Henri Valentin that includes a rear-facing trombone in what appears to be an attempt at a historical representation of a Palestrina-era performance (see far left of below image; public domain) (L’Illustration, vol. 9, May 1, 1847, p. 137).
1848—Paris, France: Georges Kastner’s treatise on military music, Manuel Général de Musique Militaire, features illustrations of a number of different types of trombones used in military music, including rear-facing valve trombone (see below image; public domain) (Kastner, Militaire Pl. XVII).
c. 1850—Bassano del Grappa, Italy: The firm Remondini publishes a print of military infantry and bandsmen. The band may represent Austro-Hungarians. Included among the band is a rear-facing trombone (see detail and full image below; public domain) (Ryan 385).