Digging around on Google Patent Search has yielded a few more interesting finds! Using the search terms "crossbow gun", I found the following:
This one, US Patent 1,704,810
, is from 1929 and is for a very basic slingshot crossbow:
This second one, US Patent 1,866,926
, is from 1932 and includes pulleys(!) as a draw-length extension, intended to keep the width of the prod as narrow as possible:
Once again, I have to say, the resemblance to weapons produced in modern times by Jörg and others is uncanny!