Pre-Hartnell Doctor - The John Hurt Doctor could have been an awful person, and decided/promised to reform himself, and dubbed himself The Doctor in accordance with that Promise. Then, he went on to betray that promise, until he Regenerated in Hartnell-Doctor.
Pre-Pertwee Doctor - We never saw Troughton become Pertwee, maybe he became Hurt and was even more bitter then Pertwee's Doctor was.
And of Course the Post-McGann/Pre-Eccelston Doctor theories, when have already been delved into.
I think any of these could be made to work well, I don't really like the idea of a Future Doctor 11 hasn't met yet, though. If it was The Valleyard or something like that, that would be OK since The Doctor already has had dealings with him, despite him being a Future incarnation
About killing him after 13 Incarnations, nah...They'll either ignore it, let the SJA "537 Lives" (or however many it was) line explain it, or come up with a story to give him more life(s)