Joe, I'm sure this is not an issue with the 37 pickup or later pickups up to 46. The issue is the relationship of the axle to the centering bolt of the spring pack. The later trucks after 47 plus the passenger cars, had a 'pivot' that was behind this centering bolt. This made the later rear ends off center in the wheel well when swapped in. Your original 37 truck axle pivoted directly over the centering bolt so you shouldnt have a problem.
On the 57 car rear end, you probably will have to cut off the spring mounts and swap in a kit or make new, don't force the springs out to fit. I had to use lowering blocks with both axles I've used on my 46 as the original cast iron mount was taller. Have fun.
