37s are pretty close to stock tire size, and you won't have any reliability issues, nor do you need the springover. 39s will run with no rubbing without the springover. If you do the springover, you can fit 44s, and the stock axles will be reliable unless you do unwise things with too large of an engine.
If you want 4-wheel disc brakes, then you're probably better off swapping in newer axles.
There's plenty of aftermarket support for the stock axles, as they're standard dana models, so you have a full choice of lockers (ARB, eaton, detroit, lockright, aussie, several brands of posis,... take your pick), gears, etc. For crawling, the stock 5.88 gears should be great.
You won't need high-angle driveshafts. Toys are little and cramped and have short driveshafts with bad angles. These aren't Toys.
I'm not familiar with that engine, so can't comment there.
Bobbing vehicles is a really, really bad idea. If you want a short vehicle, start with a short vehicle. A full 8ft bed makes a vehicle much more useful, and harming the usefulness of a vehicle is always a bad idea. Keep it a useful truck!
--Randy