"What doesn't add up is that over the last 50 years the Doctor has had a fair few regenerations and yet 200 years hence it's still Matt Smith..."

Yes, but you're thinking in linear time. It doesn't mean that he's been Matt Smith for 200 years -he could have got there next week (or 50 years ago) without actually living through those 200 years (unlike poor Rory, who had to live 2000 linear years as a Roman centurion). After all, when the Tardis takes the Doctor back in time, he doesn't revert to being Hartnell, Troughton, Pertwee, Baker etc.

It's probably quantum. Most things seem to be these days.