I will say that I'll bow out if we start playing canon characters. That's just not my cup of tea. I will also say that we need to set a certain "spoiler minimum"; i.e. we can talk freely about everything up to AFfC without fear of spoilerage.
However, I'm all for some small original story in the canon. Allow me to pitch a few ideas that I feel fall at the cruxt of major events and so have a lot of story/drama potential:
-- A Night's Watch ranging north of the Wall in the months before the desertion of Gared and the deaths of Will and Ser Royce. Wights, wildlings, and white walkers are likely. Male characters are easy, but female characters would have to be wildlings or some southron with an extraordinary backstory.
-- A small, fictional hold in the Riverlands at the onset of the War of the Five Kings. We could play soldiers, villagers, nobles, or others.
-- A small enclave of nobles in the Red Keep at some point between Ned Stark's execution and SPOILERS FOR ADwD Cerse's imprisonment by the Sparrows or Kevan Lannister's assassintion END SPOILERS. We could be from far flung corners of the Seven Kingdoms, from across the Narrow Sea, or be from the same region. Our characters may be feuding, bonded together in a coalition, or pitted against each other by politics. This would be more freeform than the others and require more effort on the part of the players.
-- Mercenaries from a fictional Company fighting in any of the major battles that occur.