Regarding the push rod, to be sure there is enough travel in retract direction of the master piston, there should be a squirt of fluid out of the bleed hole in the reservoir when the pedal is pushed. It often results in a fountain shooting out of the master making a mess if you push the pedal quickly. The cover needs to be off so you can see it. Push gently.

Do you have adjustment in the rod? Adjust it so there is a little free play in the rod when the pedal is all the way up. The piston in the master will be against its retaining ring at the front of the master. Bleed things, then adjust the play just out. If you do not have adjustment in the rod getting the right length can be near impossible. It needs to be correct within perhaps .030" or less to work correctly.

A master cylinder from a drum brake system should have the residual valves in the outlet ports already, there should be no need for external valves. I don't know what happens if there are two valves in line but I would make sure that there was only one.

Mac :{)

1962 K10 short step side, much modified for rally
1969 T50 fire truck, almost nos, needs a few things