It appears you have the original 4 speed non synchro transmission. If you have a 56 engine, I believe it is an easy job to get a 4 speed SM 420 Trans to replace the old trans. There may be some bell housing, starter Flywheel issues to solve. If you upgrade to the SM 420, there will probably be some drive shaft issues, especially if you have an enclosed drive shaft.
There is one bell housing , I think a 1947, that allows this link up to happen easily.
I upgraded on my 1 Ton with an open drive shaft. I had to get the right starter, with the right bell housing with the right flywheel. I believe an SM 420 will bolt to the 56 bell housing and everthing will fit in the engine compartment. I had to put a slight benb in the Stick shift for clearance, and shorten the short drive shaft.
