Again, not a bad start.
except have it where the Doctor and the Master are not the only Time Lords left.
Already stipulated.
I would get Patrick Stewart to show up as the Meddling Monk,
An inspired casting choice, but the Meddling Monk would need some serious reimaging I think. He should be emotionally scarred, transformed, by the Time War. Maybe he is dedicated now to 'righting' the wrongs of the Time War, but perhaps with a callousnes about the consequences for impact on people in the here and now.
and Gillian Anderson to show up as the Rani.
No, this is not a good choice, no no no. Actually, Alex Kingston would have rocked as the Rani. Have to think whoelse might be a good fit in the role - oh, if we want to go with 'American Casting' I could see Jennifer Beals in the role.
I would also resolve the stories of Peri, Nyssa, Mel, and Ace.
I think not. That isn't going to mean much except to the hard core. I wouldn't want them to show up for just 'fan service'. However, if there were a good reason, then sure. Sarah Jane Smith and Elisabeth Smith was a special case. She was, in the end, THE companion. The only ones who rise to this level of importance to show up in the renewed series by my lights are Alistair Lethbridge-Stewart (Nicholas Courtney) and Romana (should be a different actress, though - a new regeneration).
Oh, there is one special case of a story that at some point needs to be tied up in some way, that of the FIRST companion, The Doctor's 'grand-daughter', Susan. That is a gaping plot hole in the series that I think needs to be addressed.
Faction Paradox would also show-up as would Iris Wyldthyme.
They would be interesting, but hard to fit in, I think.
In the story THE END OF TIME, we would see the rise of Rassilon, the basis for the Doctor leaving Gallifrey,
That would be cool.
and a group of Time Lords being able to break out of the time loop.
I don't know - this could be good or bad.
The leader of the Refugees would be Borusa, and we would find out why he and the others were put into stasis.
No, just no. Borusa has run his course.