I don't think a non-synchronized 4 speed transmission will bolt up to your 3 speed bell housing. If my memory serves me correctly, both the center bearing retainer diameter and the mounting bolt pattern are different.
All 1937-early 1947 1 1/2 ton trucks used an open driveline.
Given your situation, I think the 3.55 ring and pinion swap would be the most expedient.
