A reoccurring issue with time travel in Doctor Who is that the main characters should know how things turn out. Sarah Jane Smith in ‘Pyramids of Mars’ is confident that Sutekh won’t destroy the Earth in 1911 because she is from the 1980s and Ace wonders why she hasn’t heard about the Daleks invading London in the 1960s in ‘Remembrance of the Daleks’.
A similar situation arises in ‘Kill The Moon’ where Clara believes that the moon won’t be destroyed because they’ve visited the future and the moon is still there. Her suggestion is that they just leave because everything will work out.
The Doctor indicates that he doesn’t know what will happen and gives possible explanations of what the moon they’ve seen in the future was. He goes on to explain that he can’t tell what happens to the moon because that hasn’t been decided yet.
The impression given is that this is an embarrassing confession and also hints that the Doctor views time differently. Presumably all Time Lords experience the same phenomena, which could have an impact on your own campaign.
The Doctor describes this in terms of being able to see time. Specifically he states that ‘litte eye blinks’, that things don’t look the same as other things. They are fuzzy, unclear and grey.
Later, when the decision has been made, the Doctor closes his eye and is able to relate how these events lead humanity to spread across the universe. It is as if he is watching the new timeline unfold before him.
Previously we might have believed that the Doctor’s knowledge of history comes from experience or things he has learnt. This new information would indicate that rather he is ‘looking’ backwards or forwards. This could apply to his own personal timeline.
This might be why the Doctor suggests that the moon they’ve encountered in the future was a hologram or a picture despite the fact it couldn’t possibly be because his 2nd incarnation was on the surface of the moon after 2049 (just to cite one example). At this moment the Doctor doesn’t remember those events possibly because he never remembers anything, he only looks.
These blind spots could explain moments in which the Doctor doesn’t recall things he really should. For example he isn’t sure if the events of ‘Aliens of London’ is when humanity first makes contact. At that moment history is in flux and he is incapable of remembering his past experiences of 21st history because his mind doesn’t work that way.
This could explain why in multi-Doctor adventures each incarnation doesn’t retain the memory of going through the experience as their younger self (with the exception of ‘Time Crash’). At those moments his ‘little eye’ has blinked and he can’t see his past or how things turn out. The talk of merging and untangling timelines is just to cover this mental flaw.
The TARDIS usually takes the Doctor to moments where his presence (or that of his companions) affects the outcome. Any knowledge the Doctor should have about those events is locked off to him until things are resolved. The reason he refuses to leave until this is done is not because of the web of time but because it would leave him blind to time.
The exception are fixed moments in time. These would be events which aren’t in flux unless history was massively rewritten. These would be akin to big landmarks, easy to from a distance. This explains why the Doctor retains his knowledge of how major historical events will play out even while they are still occurring around him.
The web of time is less an essential part of the structure of reality and more of a roadmap for Time Lords. They need fixed points to follow the paths history will take. If those thing are changed they become lost and confused.
We could interpret the collapse of history in ‘The Wedding of River Song’ as occurring almost entirely in the Doctor’s mind. The only real events are those at Lake Silencio when River changes a fixed point by refusing to shoot the Doctor.
When that happens the 11th Doctor’s ability to see past and future is disrupted to the point where he sees everything happening at once. This isn’t actually occurring, rather his brain can no longer interpret what is around him. Only by restoring that fixed point does his ability to perceive reality return.
It possible that a Time Lords can bring a future into focus while events are in flux the more likely it is they’ll exist. In ‘The Curse of Fenric’ the 7th Doctor is aware of the toxic world that the Haemovore will unleash but he doesn’t have to have visited it. At that moment, when Fenric was so close to succeeding, he could see that future ahead of them.
Similarly in ‘Pyramids of Mars’ the blasted wasteland that the 4th Doctor shows Sarah Jane Smith could be a projection from his mind, thanks to the TARDIS telepathic circuits, showing what he can see with his ‘little eye’.
The Doctor obviously has some awareness of when those events resolve, even when he isn’t present. The moment that Clara makes her decision not to detonate the nuclear weapons the Doctor arrives to rescue them in the TARDIS. Where ever he was his vision must have cleared to allow him to navigate to that moment.
This interpretation drastically changes how Time Lords should be perceived, making them far more alien. While they give the impression that they know things about the past or future they are actually reliant on what they can see, which can be affected by events around them.
Gameplay wise this could be justification for a Time Lord to be able to spend Story Points to be allowed some insight into what is going to happen based on current events. The GM can refuse, indicating that things are still in flux.
The difficulty of piloting the TARDIS can also be increased when events are in flux. This can persuade PCs to resolve a situation before they leave. It could also be an adventure hook, with the Time Lord finding that the path through the vortex is unclear until they’ve landed and resolved an important flux point.
It could be that the Doctor’s piloting skill didn’t increase. Rather once he actually started to get involved he was able to see more clearly, revealing new routes to take through history. Indeed the 3rd Doctor’s exile might actually have been a way for the Time Lords to map out the events of the 20th century, rather than just being a way to repel alien invasions.
This allows a campaign to be as much about exploration as it about defeating the bad guys. Each time they resolve a situation they discover a little more of history, making it easier to reach the next unexplored territory.