According to How did Clara end up on Gallifrey?, it’s just the Time War that is time locked. So why does Eccelston's Doctor tell Rose:
My whole planet is gone. My people, my family, all gone. Don't you think I want to go back and save them?
Why hasn't he ever gone back to before the war?
All the other Doctors basically see Gallifrey as gone from them, and when you say the Doctor cannot go back on his own timeline, there will have been plenty of time periods he could go to; maybe to a time before they could regenerate, or maybe when Time Lords were using Tardises — as in "The Doctor's Wife" she says to Matt Smith:
I was already a museum piece when I stole you