When you replaced the MC, did you bench bleed it first? If not, take it off and try doing that first. Usually there are instructions with the replacement that explain how to bench bleed a MC.
Do you have access to some kind of shop manual procedure for brake bleeding? Every vehicle is a little different, in the order you have to bleed the lines in, and some may have accumulators that need to be bled separately. ABS equipped vehicles sometimes require the manufacturer’s scan tool to set the ABS into a special mode, otherwise bleeding is impossible. On some vehicles the configuration of the system is problematic and pressure bleeding of the entire system is about the only way to do it. If at all possible, try to find the manufacturer’s bleeding procedure for this vehicle.
It won’t be possible to eliminate a squishy pedal if there’s anything moving in the brake system. Make sure the rear drum brakes are tightly adjusted, drums to shoes, so if you adjusted them a little more tight the wheel won’t spin freely. Sometimes if all else fails you have to take everything apart and see what’s causing the movement. If so, start at the front disc calipers as they tend to get into stuck-in-the-wrong-place configurations more than drums.
If you’ve changed wheel cylinders or calipers, make sure you haven’t installed them upside down. I know it seems impossible, but on many vehicles it is actually quite possible to do this. Often involves putting the one supposed to go on the right side on the left, etc. The way to tell it is correct, all the bleeders should be on top of the calipers/cylinders, and point up.
FYI, when I bleed my Corolla, starting at the longest line I open the bleeder screw, the push on the brake pedal with my hand only (not my foot), and only to about the 3/4 way down position, not all the way down. Then – keeping the pedal at that 3/4 position – I close the screw. Repeat until there’s clearly no more air coming out. Then move to the next longest line. For me that has always worked. Press gently and slowly, like you are squeezing toothpaste out of a tube, no pumping on the brake pedal at all.
Brake bleeding can be very frustrating. Suggest to keep calm and approach it scientifically. If there is nowhere, no gaps, for anything to move and no air it the hydraulics, you pretty much have to get a firm pedal. You might have to figure out a way to eliminate which wheel it is, one by one. Best of luck.