I've been reading up on regeneration on the Wiki and found a few relevant tidbits:
http://en.wikipedia.org/wiki/Regeneration_(Doctor_Who)
Quote:
“It is stated in The Deadly Assassin (1976) that a Time Lord can regenerate twelve times before dying (enabling thirteen incarnations in all).”
So it's definitely a fixed figure.
Quote:
“it is explicitly stated by the Fifth Doctor in Mawdryn Undead that he has eight incarnations left, and in The Five Doctors Peter Davison's Doctor (introducing himself to the First Doctor) says that he is the fourth regeneration, meaning that there have been five of him. Again in The Five Doctors, the First Doctor refers to himself as the "original" and in Doctor Who, Paul McGann, with Sylvester McCoy on screen, states both "A Time Lord has thirteen lives and The Master'd used all of his."”
So it looks like the regeneration between Troughton and Pertwee is definitely considered a proper regeneration (thus answering my OP).
Quote:
“The John Peel-authored book The Gallifrey Chronicles attributes regeneration to a "nanomolecular virus" that rebuilds the body. The audio play Zagreus attributes regeneration to "self-replicating biogenic molecules" designed by Rassilon, which do much the same thing, with a built-in limit of twelve regenerations to prevent the molecules' decay. According to the Virgin Missing Adventures book The Crystal Bucephalus by Craig Hinton, Time Lords have triple-helix DNA: the third strand was added by Rassilon to make regeneration possible. These varying explanations may or may not be compatible with each other, and like all spin-off media, their canonicity with respect to the television series is unclear.”
Quote:
“In The Deadly Assassin (1976) it is stated that the Master has used up all his regenerations, hence his decrepit appearance in that serial. He is in attempting to use the artifacts of Rassilon to obtain a new cycle, but the process would destroy Gallifrey, so the Doctor intervenes. The Master subsequently takes over non-Gallifreyan bodies in order to extend his life. The first is a Trakenite named Tremas in The Keeper of Traken (1981). In The Five Doctors (1983) the High Council of Gallifrey offers the Master, who is now possessing the body of a Trakenite, a new regeneration cycle in exchange for his help, although there is no indication that he actually received this new cycle.”
Clearly it is possible for the Time Lords to bestow extra regenerations and we also know it's possible to transfer regenerations from one Time Lord to another (as River did to save the dying Doctor). So, however it works, I'm sure the Doctor would have no problem finding a way to extend the limit.