As for pulling the wool over time's eyes.

The fixed point isn't his actual death in this case but history recording it.

If JFK had successfully faked his death history would have played out pretty much the same.

If some someone had successfully managed to fake JFK surviving his death history would have changed.

We have a lot of on screen evidence of the Doctor having companions we don't see and he lies.

He may not really be as old as he makes out or even older (he seems to forget he claimed to be almost a thousand years old as the Sixth Doctor when he is the Ninth. He forgets he claims to be a Doctor for thousands of years when he in his third incarnation and as for the other incarnations before William Hartnell seen in The Brain Of Morbius he forgets them too).

The Doctor has always been an unreliable narrator, which is why arc based stories don't really work when they hinge on things he says.

I don't even see why he has to keep his head down.

Now that the universe assumes he dies in his eleventh form he can wander around in much the same way he already has and everyone will assume those adventures take place before he dies.

It was a mess though.

Why bother coming up with a storyline where time has collapsed onto itself when the production team clearly don't have the budget to explore the possibilities of such a world?

A whole series could have been set in that screwed up world.

Instead we got a few moments of visual madness and then a base under siege story that could have been set anywhere and anywhen.