Short starters date way back, as they were used as a means of starting oversized, unpatched balls. As patched balls took over, I think they died out and then were revived for use with patched balls, possibly as a result of some military textbooks plagiarizing older publications that mentioned their use for unpatched balls.
Earliest mention of a short starter on a patched ball is 1780, in a German text talking about civilian guns. By the 1790s the Austrians and British are issuing mallets with their military pieces; however, the Austrians used a very different method of loading their Jager rifles that involved keeping their iron ramrods on their belts (no provision for a ramrod on the gun itself) and the British mallets were issued only to every second man IIRC, which I suspect means that they were intended to be used to deal with dirty bores, out-of-spec ammo, and other battlefield contingencies rather than a routine method of loading. The use of a mallet for loading first appears in print on this side of the Atlantic in the first years of the 19th century, as far as I know, in a military treatise, from, I think, New England.
In contrast, there are a number of descriptions and accounts from the period 1750 to 1810 that describe loading without a short starter. There is a German text from about 1750 that describes how to hold the ramrod so as not to risk breaking it while starting the ball, to start with. Around 1790, Isaac Weld, who was apparently familiar with fowlers but not rifles, describes for his readers every point in which an American longrifle rifle differed from an English fowling piece, including the use of greased patches and rear sights (he likens rifle sights to surveying equipment), but never mentions the use of short starters. Neither does Hanger, for that matter, though I'm unsure how significant to take that omission. Audubon, writing about a hunt around 1810, describes the use of a knife handle to start the ball. I am not aware of any documentary or archeological evidence for short starters or mallets prior to at least 1800 here in the US - I have yet to run across any mention of them in the Draper manuscripts or other first-hand accounts of Indian fighting, any probate records, wills, etc., nor have any been recovered from archeological sites, either. Honestly, if they were in widespread use, I'd expect to see at least a couple off-hand references to them in the Draper papers and other narrative sources, if nowhere else, like a time that someone dropped his short starter while trying to load in a hurry and consequently had to make a run for it.
Given the evidence available, I think that we are looking at two different traditions of rifle use here. The old, mid-18th century style didn't use specialized short starters, is the one that was brought over and remained established through the remainder of the 18th century. I'd call this the "Kentucky" tradition, and I suspect that it remained predominate out on the frontier well into the 19th century, as I don't recall any mention of short starters during the Fur Trade either, nor are there any that I am aware of associated with Hawken rifles, etc. The other tradition of using specialized starters, mallets or short rammers, originated in Europe sometime later in the 18th century and came over here in a military context early in the 19th century. I suspect that got adopted by civilian shooters because of its usefulness in loading tight, accurate balls for shooting matches.
Hey, has anyone ever turned up an Appalachian short starter? Can't recall seeing one in John Rice Irwin's book, and he has quite a collection of shooting stuff in the Museum of Appalachia. If not, that might be significant....
Edited to add: I see that there is one supposedly in the Museum of the Fur Trade. Be interesting to know more about the provenance of that one.