Well, the general rule is, when something is working, you do something and it does not work anymore than you assume its related to what you did.
In this case, it sure sounds like something is misaligned or binding.
However, there is always the possibility of a coincidence here and something is hydro-locking the engine.
Go ahead and pull all the plugs and see if that lets it turn over. If so, what squirted out the plug holes? Gas or water?
If it still does not spin, then its almost certainly going to be something related to the transmission swap.
The next thing to try, is to get someone to hold down the clutch while you crank it. If the clutch is working, that will tell if its in the tranny or not.
I suppose its possible that the shaft did not go into the pilot bearing and the clutch disk is binding.
Don't see how you could have bolted it all the way up if so.
The fact that it cranks for about 3 seconds at first sure sounds like hydro-locking.
I suppose if the transfer case were locked, there might be enough slack in the gears and bearings ahead of it to let it crank that far......