Have a 47 coupe with 3:55 torque tube out of a 53 powerglide equiped car, she runs fine and loves the hills. As mentioned, the problem with your car and mine is that you can't just swap the trans or rear, you need to gut the entire driveline to make any major changes like open driveline. The trans you have is also the rear motor mount, stock side mounts on your car are junk, you need some expert advise.
You should contact Buffalo Ent. right up there in your neighborhood, for how-to and he has a zillion great kits/ideas for all chevs of your vintage. He has trans adaptors motor mounts, everything you'll need to swap anything into your old Chev.