I personally think the short starter has been in use since Americans first started using patches with roundballs. Seeing as there were few micrometers and dial calipers lying around then it would have been easy to mismatch a patch and ball, and to get that thing on down the barrel the natural tool would have been a short stick and hammer, or rock. And I also think our forefathers were clever enough to see the benefit of having such a tool close at hand, at all times. Even if they were using a loose P$B combo and a coned barrel, things still happen.
Just because none of the "Wooden" (think rot and time) short starters have survived or been regularly documented, doesn't at all mean they were not used.
Remember, a lot of critical stuff was forgotten during early centerfire years concerning ML guns. Only in a few areas were these weapons still in regular use, and those users were often illiterate.
The study of this stuff is a lot like archeology. A lot of guesses and supposes. And in a few years they rewrite the history books again because they have learned they were wrong about something.