I think you are onto something with the master cylinder.
Brake systems can be tricky to diagnose at times.
Bleeding with the car running just runs the risk of blowing a hose, line or piston, because the booster is way over assisting.
Since there is no air in the system after your double check, about the only thing left would be the master, especially after confirming there are no line, hose or piston leaks.
As for a caliber not working, you'd know by looking at pad and rotor wear.