just some food for thought, I recently picked up a 72 C30 with factory power disc/drum setup with a faulty master cylinder. Replaced the MC, blead the system and everything was great for about 5 miles, then my pedal went to the floor JUST as I was parking the truck at my house. I assumed I lost a hose or wheel cylinder. Nope... When I parked and turned the car off, as soon as the booster was evacuated of vacuum (pumped brakes when car was off) the pedal got perfectly firm, and would even stop the car when rolling with engine off. as soon as the truck was on, the booster would assist me in pushing the pedal strait to the floor every time. Brake fault dash light would also turn on. (Happy to see it worked!)
spent two days bleeding every corner and at the MC and Prop valve. no air, clean fluid.
Not seeing many options, I bought a second new (reman) master cylinder. was VERY careful to ensure thorough bench bleeding (20 minutes at least, I was to be CERTAIN it was clear of air!) I put it back on the truck, was able to actually only bleed it at the MC and the Prop Valve, and brakes were prefect.
I am not saying your issue is EXACTLY the same as mine, as my issue was with stock (rebuilt) components, but if you have a firm pedal without your booster helping, and when your engine is on the booster helps push the pedal to the floor it could very well be the MC (air or fault). I think in my case my MC was failing internally and allowing fluid to pass between the internal seals, but I could see air causing a similar problem.
If your rear brake shoes are properly adjusted, and your confident there are no leaks in the system anywhere I would look at the Master Cylinder. Generally, master cylinders are only two nuts and two hoses, I would start by taking it off the truck, putting it in a vice with a
master cylinder bleeding kit (click here for link if your MC didn't come with one) and spend some time carefully bleeding it until your comfortable there is no air in it. Its possible to bleed it in the truck but its way easier to control the 3/4"-1" slow piston pushes when its not in the truck.
If you can blead it totally free of air, and your still having issues... id make sure your drum shoes are adjusted and then start thinking about if you have a faulty master?
Booster shouldn't be your issue, it helps push, it seems to be doing that just fine.