the newer 383 has a 6 bolt crank flange, while the older 361 has an 8 bolt crank flange, and as has been already stated, the 361 crank flange is 1" longer than the newer 383.
so if using the 383, some kind of an adapter will have to be made to mate the crank to the 361 flexplate. that may, or may not be hard to do. it may not be even possible, i don't have a crank in front of me to inspect as to the possibility of such an adapter.
the 59 engine mounts will have to be used on the 383, as they are an entirely different style of mount than the newer 383 uses.
the accessory mounting holes on the end[s] of the 383 head[s] may be different than the 361 heads. i'm just stating this as a precaution if the OP decides to use the 383 heads to get the 361 running. also, the 361 heads may be closed chamber heads as well, while the 383 may have open chamber heads. [i don't remember what the 361 had for heads.]
i think this post may be repeating myself.