How do you explain 42, then? His organism was apparently changed by the sun particle whatever blah thing that possessed him. And yet, seconds after Martha saved the day, he was back to normal.
*admits that we have a problem here*
What if, he didn't change back by himself, but it just happened naturally, because the particle thingy (which was a lifeform) left him before the change was complete. So by leaving the Doctor he just went back to being normal. But it had nothing to do with his regeneration abilities. Does that make sense?

I like the idea of healing no/regeneration yes, because it would explain the Master's death and the other small injuries.
Healing is just recreating the 'same' cells again (DNA wise), while regeneration is rewriting the code of the DNA. So they are two different things. (at least to my layman-opinion)
But if you come up with another working theory, I'll happily follow you! :-)

And, well, the watch thing... yeah, that's... mmmhhh. Maybe he needs it, because regeneration is still rewriting TIME LORD DNA, while changing into a human involves becoming a different SPECIES. Which is even more complicated. That's why he needs the machine. (???) And maybe that's why he loses his memory too. Because it's much more invasive. Like trauma or something???

*is dloading classic Who every time she can*