According to my 1937 Engineering manual, the '37 steering box is really different then the '36. The ratio is up from 14 to 16 to 1, the whole unit is turned over, and the mounting is different plus forward from where it was in '36. Pitman shaft is shorter by 5/8" on the '37 then the '36.
Sounds like it would some work to change one out, but it you had them side by side and could get a good look at them, it might not be that hard.
The frames were redesigned for '37, so they are not the same.
Joe