The Doctor is not present when the guards arrive, and we can only speculate what happens to him next. Maybe he escapes from Gallifrey, and spends the subsequent three incarnations as a fugitive. What is certain is that the Doctor eventually returns to Gallifrey and is born from the Loom of Lungbarrow as the Hartnell incarnation, with little or no memory of having lived before. As far as his cousins are concerned, he's a new person. Perhaps this was imposed upon him as a form of punishment - but in the absence of any contradictory evidence, I prefer to think that the Doctor has done something clever to elude his pursuers. He has regenerated, but arranged things so it appears he's being woven from the Loom. The fact that he still has a navel shows he's really the same womb-born Time Lord as the previous incarnations. (And indeed in Lungbarrow, the young Doctor says that he can remember being in the Loom, waiting to be born, which is dismissed as "impossible".)

However, we cannot dismiss completely the notion that the Time Lords themselves wiped the Doctor's memories and effectively let him be born again as a new person. They certainly seem to have form for this - evidence revealed in The Timeless Children suggests that the Doctor's history may go back much further than we hitherto suspected - maybe even to an origin preceding Gallifrey and the Time Lords - but the veracity and reliabilty of this information is as yet uncertain. Nevertheless, we have seen the suggestion of multiple regenerations.

	We learn that eventually the Doctor will start working for a shadowy Time Lord organization known only as "Division", seemingly through several incarnations - before finally going on the run from her employers. It is this incarnation who, whilst in hiding, crosses paths with the thirteenth Doctor, as we see in Fugitive of the Judoon.

Though the true history has been hidden, overwritten and destroyed, there are strong clues that the Division wiped the Doctor's memories to cover their tracks. But was this the same incident as described above? Or was it perhaps one of several, repeated mind-wipes and resets that have occurred throughout the Doctor's life? We simply don't know yet.
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In an attempt to reconcile all the evidence, I would suggest that this is what happens in The Black Hole: The Monk has discovered that the Sontarans are about to attack Space Station Camera and slaughter the crew, so he decides this will make a suitable trap to send the Doctor into. It's made abundantly clear in dialogue that he knew the Sontarans would be there - and as Jamie says: "you sent us there to die!" We can assume the Monk also detects temporal distortions there from the time travel experiments, making it a totally plausible environment into which the Time Lords would send an agent. The implication from Deathworld is that the events seen in The Two Doctors do indeed play out here. But upon their return to the Habitat, the Doctor and Jamie seem more vague in their recollections - they know there were Sontarans and that they avoided a trap that might have killed them, but they don't talk about the time travel experiments or the genetic modifications the Doctor underwent. So we could suppose that when Death returns the Doctors to their proper timestreams at the end of Deathworld, as well as erasing the events of that story, some of the surrounding events are altered too - becoming unstable parts of the timeline. (Certainly, Death implies that he has control over the events from which the Doctor was taken.) When the Doctor gets back to the Habitat, via a number of unplanned detours, he's only got the vaguest recall of what happened. At the end of The Black Hole, it's implied that (the real) Pavo wipes the Doctor's memory of it all anyway, so neither he or Jamie will remember any of it.

Now, let's jump ahead to World Game. The quantum instability caused by the timeline erasure means that, as it appaers now, the Doctor was never on Space Station Camera and never put a stop to the time travel experiments. In sending the Doctor there to see Dastari, the CIA are (intentionally or not) also helping to restore the damaged timeline. The Doctor asks for Jamie as a companion, which of course means undoing the memory wipe that was done on Jamie at the end of The War Games. I reason that the Doctor doesn't want Jamie to have to go through all the heartbreak of their separation again, so he suggests that the CIA reset Jamie's memory to an earlier time. But when considering which point they should roll Jamie back to, some subconscious memory of The Black Hole comes back to him - the mention of Dastari and Space Station Camera triggering the thought of Victoria studying graphology - so he gives it as the new backstory for Jamie. And so the events of The Two Doctors unfold from there.
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So while the Trevor Martin Doctor carries on as a sort of off-shoot incarnation, the Pertwee Doctor remains behind - still irradiated, still dying. The burst of energy from the bi-generation may have helped to temporarily hold the effects of the radiation at bay, allowing the Doctor to carry on for a while - although there are still clues that all is not well. Perhaps one of the effects is a gradual breakdown of the morphic structure of the Doctor's body - which accounts for why he looks slightly different from normal in The Story of Aladdin. (Other than the fact that stuntman Terry Walsh is standing in for Pertwee here.) And then the deterioration continues. In Ancient Whispers, the now weakened Doctor is unsure of his chances of achieving a successful regeneration without outside assistance. Finally, he can't even operate the Tardis, and has to rely on the ship to bring him back home. (Although in Love and War, we learn that it takes him ten years to finally make it back to UNIT HQ.)

I don't intend to speculate as to whether the Trevor Martin incarnation continues on his own timeline and has further regenerations. As with the David Banks version, I suspect eventually the biodata will be re-absorbed into the Doctor's primary timeline. Maybe the Time Lords get involved to sort things out. After all, they know who the actual fourth Doctor should be - especially since he became President and saved the planet twice, they've got a vested interest in ensuring the Doctor's timeline remains stable.
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The story does seem to be set in a different continuity, one in which the Time Lords are all but extinct. What I find interesting about this is the way it echoes later developments in the Eighth Doctor novels, particularly in the aftermath of The Ancestor Cell, when there are said to be only four Time Lords left alive in the universe - one of whom is the Minister of Chance. It's as if the events of that War in Heaven are so cataclysmic that they have repercussions in the past as well as the future. (In fact, if this had been an eighth Doctor story, I doubt there would have been half as much controversy around it.) So maybe that's what's going on here, future events rippling back and overwriting the established timelines. One presumes that the ending, and the Doctor's defeat of General Tannis, cancels all that out and puts events back on their proper course.

I've placed the story near the end of the seventh Doctor's life. This is quite a nebulous period, perhaps a long time after any other recorded adventures of this incarnation, and we may never know what leads to these events. Obviously, the Doctor does not actually die at the end of the story - and it's made quite clear that they never find his body. I believe that he withdraws from circulation following this, and keeps a deliberately low profile. (Doom Coalition suggests that the Doctor turns into a sort of errand boy for the President; and in his final few appearances, he appears quite low key and introspective.)
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Of course, a different version of the same adventure occurring to more than one Doctor is nothing new. I've already dealt with The Ultimate Adventure, Shada and the redrawn TV Comic strips. As with those, I'd suggest that the Doctor is drawn on some subconscious level towards such areas of quantum instability, as if feeling the need to restore missing sections of his timeline. Alternatively, it may be that the Tardis is deliberately seeking out these space-time discontinuities. After all, when the Doctor activates the chameleon arch, he leaves all the details to the Tardis: creating a credible backstory and finding the right setting for the John Smith schoolmaster persona. Though the Doctor may not himself recall the events of the original Human Nature, we can imagine that the Tardis on some quantum level retains that knowledge in its memory banks, and automatically draws upon it to create the Doctor's new human form; and in locating a setting in which to place him, homes in on an area of quantum instability to try and protect the integrity of the Doctor's timeline.
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But despite the subconscious dream nature of these encounters, it's stated that the Doctors have the ability to control the memory Tardis, and even to be able to use it to go on to new adventures. It's really not clear how this is happening. Are they actually having adventures in the "real" world? Is each Doctor resident in the Tardis at a different time? Or is this all somehow happening at once? When they wake from their dream, do they return to their own timelines? Do they go back into their own conscious forms? It continues to be a mystery.
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