I had developed this theory to explain the previously unknown John Hurt Doctor. Of course, with the release of the Night of the Doctor my idea completely falls apart. So instead I present it as a possible scenario for the game.
My idea was that John Hurt was definitely the Ninth Doctor, but the product of the Season 6B timeline.
Season 6B is that bit of continuity wiggle room in between the Second Doctor's last appearance in War Games, and the Third Doctor's first appearance in Spearhead from Space. Instead of exile on Earth as the Time Lords had decreed, the Doctor became their agent dealing with secret missions for the Time Lords. That apparently lasts quite a long time for the Second Doctor, who is visibly aged when he's seen in The Two Doctors alongside a much older Jamie McCrimmon. Though eventually the Second Doctor either died in action, or failed the Time Lords in some manner. Either way they follow through with their decreed fate for him and he becomes the Third Doctor we see in Spearhead.
What if that was not the case?
Instead, the Doctor regenerates into a completely different person. This Other Third Doctor is forced to remain in the service of the Time Lords as an agent of the Celestial Intervention Agency. The Doctor has proven himself far too valuable, and the Time Lords are getting rumblings of dangerous things happening through time. They have already foreseen the threat the Daleks pose to the universe, and the Doctor is the most logical agent to try and deal with this.
So we have a series of adventures with a Doctor working (if not necessarily willingly) directly for the Time Lords through the Celestial Intervention Agency.
It could be the Time War may have already begun. It might be the adversaries in War Games may have been part of the larger machinations of various parties in the Time War to raise an army that could fight against the Daleks. The Doctor realizes what is at stake and remains part of the Time War, and in the process giving up a number of lives in the name of trying to stop the Daleks.
For a Time War themed campaign, this does give you the option of recruiting any of the classic Doctors into the War. Or you could create a new alternate Doctor tailored to your campaign, and still claim continuity.
