you have an ax5 and np231 t case. that trans is only worsted by the pukegoat ba10. that trans will not work with even a 6 cyl.
if you want a manual trans to go behind a 350 there's a ton of options, i like to look at www.novak-adapt
under their knowledge section, good info. there's some crazy strong and geared manuals from the older days great for off road, or if its a driver i'd pick an overdrive trans. i've heard that people do put the ax15 manual trans behind the 350, thats what came in wrangler's with the 4.0 from mid 90 and on untill the nv3550 replaced it.