Brake pedal goes to floor with engine running

The description above notes that the brakes are good without the engine running WHEN THE BRAKES ARE PUMPED UP. That is the problem right there; there is still air in one half or both halves of the system. The pedal should not pump up at all under any circumstances. BTW, the pedal going down SOME when starting the engine with a power brake booster is normal, but the booster is making the air-in-the-system problem worse.

I would suspect that the first MC was not bench bled, or the wheel cylinder and caliper bleeding technique is not right. Same for the 2nd MC. BTW, I would never re-use an MC unless it was absolutley known good, and any installed MC has to be bench bled prior to putting in the vehicle.

One other thing to consider is that the MC be right for the bakes front and rear. I assume you have rear durms and the MC for that will have check valve to keep the fluid from the rear wheel cylinders being pushed back by the springs.

And, make sure the fornt and rear lines to the MC are connected right; the fronts should go to the larger MC reservoir.