6(b) - or not 6(b)?

According to events in the closing episodes of The War Games, the Doctor has been on the run from his people - the Time Lords - for some time. To foil the alien scheme, he is forced to reveal his location to them - and tries to do a runner before they can arrive. He fails, and ends up back on his home planet (still unnamed at this point) to face trial for stealing the TARDIS, and for intervening in the affairs of other races.
For such a significant crime, the proceedings are dealt with by a three man tribunal only, and in rather speedy fashion. And, despite the seriousness of his offences, the Doctor is given a relatively lenient sentence (considering the tribunal has just erased the War Lord and his troops from time and imprisoned their planet for all eternity). The Doctor is sentenced to exile on late 20th Century Earth (tantamount to being sent to an open prison), and to have his appearance changed. We assume this to be a regeneration, though it isn't explicitly stated. When next seen, he is falling out of the TARDIS in an Essex wood.
Later stories, however, suggest that a lot may have happened in between the trial and the arrival on Earth - a whole set of adventures for the Second Doctor, working under duress for a shadowy Time Lord group later identified as the CIA - Celestial Intervention Agency. This might explain the low key tribunal - and those later Second Doctor appearances. Fandom has dubbed this period Season 6(b).

The Second Doctor is taken out of time by the Time Lords to help the Third Doctor when he and they were under threat from a power draining force emanating from a Black Hole - the work of Omega. Do the Time Lords now know where the Doctor was - retroactively? Could they plot his movements backwards from the time they captured him? Might they have always known where he was and only dragged him back home after the events of The War Games as he had gone a bit too far this time? Or is this the Second Doctor from events after the trial, when he is working for them? If the latter, then the most senior of Time Lords knew all about the CIA and its activities. If not from a point after the trial, then it has to be from sometime after The Invasion (as the Second Doctor knows Sergeant Benton).
We find out about the CIA in The Deadly Assassin. We assume it refers only to the occasions when the Time Lords sent the exiled Third Doctor to Uxareius, Peladon and to Solos, and later diverted the Fourth to Karn. One of the tribunal members appears to send  the Doctor to Uxareius, and Chancellor Goth also appears to have been a tribunal member. So the CIA might also have been working closely with the Second Doctor between the trial and the exile.

The next time we see the Second Doctor, in The Five Doctors, he is noticeably older. He can also pilot the TARDIS precisely. He mentions that he can't stop long and is bending the rules - having given the CIA the slip temporarily? Most tellingly, when confronted by the apparitions of Jamie and Zoe in the Dark Tower, he knows of events at the time of his trial - that they should not remember him. (The script is in error here, as they would have remembered their initial encounter with him, but the fact remains that this Second Doctor originates from a point after the trial).

The strongest evidence for a Season 6(b) is The Two Doctors. The Second Doctor is explicitly stated to be working on a mission for the Time Lords. They have given him a remote control for the TARDIS and he can again pilot it precisely. He is even more noticeably older than he was at the time of his trial - as is Jamie. He is travelling with Victoria also, and has been able to drop her off somewhere - confident of picking her up again afterwards. The CIA have obviously taken into account that the Doctor works best with human companions and have allowed him to pick up a couple of his old travelling companions.
Season 6(b) is the only way this story can possibly work without throwing Second Doctor continuity out of the window. Remember also that Robert Holmes, who wrote this story, was the writer of the first Earth exile story and he was the creator of the CIA.

As far as Terrance Dicks is concerned, Season 6(b) is a reality. His 2005 novel World Game covers the period immediately following the trial and recounts the Doctor's first mission for the CIA - to prevent temporal interference in the Napoleonic era - and it ends with him getting his old companions back and sets up his mission to confront Dastari.
Now, my remit on this blog has always been to concentrate on televised Doctor Who only, but if Season 6(b) is good enough for Terrance Dicks, co-author of The War Games and story editor of the subsequent story, then it's good enough for me. I think it is the only way to explain the later Second Doctor appearances - especially The Two Doctors.