Irons,
I have a restored '36 Chevy pickup with the 1932-36 style synchronized transmission. That was Chevy's first attempt at a synchronized trans. In its day it was better than an unsynchronized "crash" box but it's a complicated device that doesn't work very well. Also, the parts required to get its synchronizers' end play into specification have been unavailable for decades.
If I were doing a project like yours I would use anything but that '36 trans. Even a '37 Chevy trans is a big improvement over the '36 and it will accept your '36 U-joint. I found that out when I put a '37 Chevy car rear axle in my '36 PU so that I could use 3.55 gears. Here's the story on that:
http://vcca.org/forum/ubbthreads.php/topics/334876/1936_Chevy_3.55_rear_gear_convThree speed gears from Chevies up through the 1950's can be adapted into the '37-'39 Chevy 3-speed floor shift trans with some work for improved shifting.
