The Stovebolt Site Forums The Parking Lot Big Bolts 37 1.5 ton SD transmission ID?

I'm trying to determine if I can swap this 4speed for a newer SM420 with backup switch, or if I already have one installed. I'd like to either add syncs to this transmission or swap for a SM420. I believe the 37 4spd is the precursor to the SM420 and parts might be interchangeable. Here's some pics.
It is an H pattern. Granny 1st left/up, 2nd down, 3rd right/up , 4th down , reverse is little lever up and stick all the way left and down.