Beaver Bob, I just opened up a 420 trans that I got cheap, it was going to the iron heap. Man, this thing is built and very considerable in size in relation to bearings gears, etc. That could be a firm foundation for your drive train. I had the original blown up babbit 216 and decided on a 235 for my truck but a 250 should be fine, just need to make sure the bell housing fits. Ujoints and driveshaft for that rear will be real easy for a shop to cut the exact length and balance and put the yokes of your choice on there. Sounds to me you are on the right track to getting a forward direction on your 37-38. Post up some pictures as you proceed. Most of us live vicariously through other people's builds.

1953 Chevrolet 3100
261 cu inch, sm420, 3.55 rear, torque tube still,omaha orange, still 6 volt, RPO green glass, side carrier spare, all done
In the DITY Gallery
Video of the 261 running

1964 GMC 1000
305 Big Block V6, sm420, the next cab off restoration