You don't need to remove the MC to "bench bleed" it. Indeed, I always do it on the car. You much bench bleed it, like >50 pumps to get all air bubbles out. Many videos on youtube.
If nothing else, suspect the booster as post #15 suggests. I would have sworn that a bad booster couldn't allow the pedal to sink, but several people said that changing the booster fixed that problem. Perhaps there are internal parts in the valve and force path that can fall out and allow more play.
