I try not to get too working up about issues like this. Back in the 70's the showrunners just weren't as diligent about continuity as they are nowadays.
Re The Masters skepticism: I can see the time Lords being able to hand out new regeneration cycles, but doing so is a serious breach of ethics. The Master was simply doubtful the the oh-so-pure High Council would violate the rules that way.
Re Pre Hartnell Doctors: Perhaps the Doctor had a previous identity, but as punishment, or thee need to hide who he really was, he was given a new regen cycle and his memory of his old life erased. Might actually go a ways toward explaining all the Cartmel stuff.
Looks like some people need to pay better attention next time they read Lungbarrow.
I've read it three times.
Maybe I should read the thing. It must be a hell of a story if people are still quoting it and bitching when the show contradicts it after all these years.