1) TH350 is an auto. You are correct; an auto usually will not work under a CJ-5.
2) Your CJ-5 originally had a Dana 20 transfer case. If someone had a 300 in it, it was swapped in.
3) I run a 350, Dana 20, T-18 combo. It's terrific, but you do have to buy an adapter to mate the T-18 to the 350, and it's pricey.
4) I'd look at a GM transmission, too--something like an SM420, SM465, or the NP435. Of course, you'll still have to adapt the transmission to the transfer case. Novak conversions has a great deal of information on its website which should prove helpful.
5) I don't know about a full engine-transmission-transfer case set up, as I don't know anything about GM transfer cases. It would depend upon where the outputs are in the transfer case. You need a transfer case with the front drive shaft output on the passenger side and the rear centered. Of course, you could pick up the whole drive line out of, say, an old Blazer, if you were willing to/interested in swapping out axles, too. You'd need to do some fab work with cross-members (most likely) and spring perches, but that's an alternative.