I think the half stock started showing up on guns in this country after 1815 or so, probably copying the trend in european sporting arms, and yes, many New England rifles were half-stocked (often with very straight or gently curved butt-stock architecture, and sometimes using wooden under-ribs), but they were made elsewhere as well-I've seen pitures of half-stock Bean rifles, Whisker shows several half-stock Virginia rifles, and of course many of the western rifles were half-stocked. I believe the Steel Canvas book shows a few half-stocked flint rifles. And yes, they mostly used a cap on the end of the forearm. Probably your best bet is to peruse the literature and see what you can find.