Big Finish has done that idea more than a few times so we know that can work on a thematic level.You could do something interesting with a concurrent Past Doctor/Current Doctor set of series, which is having the current Doctor have a "sequel" ep to something that only just happened to Past!Doc and show how 400+ years of change might affect decisions.
Or have Current!Doc have an adventure and then Past!Doc encounter the consequences, like Seven running into the problems "Merlin" created in Battlefield, only we get to see the Merlin side of the story.
I agree that we could've/should've gotten some Eighth Doctor love during gap years but I also agree that I don't see the BBC ever running two Doctors at the same time.