|YOU LISTENING, MOFFAT?|
First thing is that I'd have 10, 1 hour long episodes (or 13 if we're being idealistic) instead of 45 minute ones. For the purpose of the explanation I'll have 13, and I'll assume Series 7 is the starting point, so Asylum onwards never happened. Nothing against Season 7; or Moffat for that matter; I'd just rather work with a Series I actually know the ending of and not have the potential baggage of the Clara Oswald arc!
Amy and Rory DO NOT return (well, they do, but I'll get back to that). The new companions are a man from the not too distant future called Samuel and an alien with the form of a humanoid woman called Katie for short. I'll get into them later.
The idea I would consider making the main story arc for the series is the companion who never was. The Doctor can't always save everyone from every disaster, we've seen as much in SJA and especially Torchwood. I think that - somewhere in the universe - there was someone The Doctor missed. Someone with great potential who would have been the perfect companion for him. She heard stories of the time he visited before, but he never returned, so all that potential turned to jet black hatred. She thought she had found someone to replace her Doctor, but he died, so her plan is to both ruin The Doctor and to compress time so her knight could return to her. It stemmed from a backstory I thought Kovarian could have, but never really did.
This arc would be the big focus of around four episodes: The first (around episode 5) where she attempts to set Time Compression, but The Doctor doesn't know who she was. The second (episode 9 or 10) she isn't directly involved in, but The Silence attempt something suspiciously similar in a desperate bid to stop The Doctor from revealing his secret at Trenzalore. The two part finale unveils (surprise) that the not-companion has at least partially been a puppet of The Silence, and time is actually devoured... Until the end of the series anyway.