I have three contending ideas - two better formed than the third. Here's the first (and front-runner so far).
TIME TRAITOR
2x6 +14 days
TEAM
LAW
ACTOR
In the first session of the game, the players have a 'typical' time-travel action-adventure on the first session, then at the end of the first session they come back to find the future all screwed up. Cue cliffhanger.
Two weeks later, they have a second session where they go back to try and figure out what went wrong, and try to reconstruct the first session using only their notes and consensus. The trick is that one of them is a traitor, and who it is isn't apparent even to the players themselves, because the betrayal happens "after" the second mission. I'm trying to figure out how it's going to work, using 'consensus points' - basically, if your version of things rules the day, you score points. The traitor is the person with the most (least?) points at the end of the second mission.
The real sticking point here is that in the second mission has to at least have *some* structure to it (perhaps it'd have to be based around a recent historical event that everyone could refer to) in order to hang the narrative on, but also have a great deal of imperfect information, so that the actions of the characters, and the recollections of the players have some real fuzziness to them.
I'm thinking that note-taking will be limited to 10 (20?) entries on a 'journal page' supplied with the game. There would also be 'checkpoints' in each session - the players have the first hour to deal with, say, making sure that Oswald gets to Dallas. At the end of the hour, it's over and whatever else they may need to recollect about the first session is lost. Since you're simultaneously playing the second session and 'reliving' the first session, there's a big chance for slippage there.
All of this makes me wonder if I need one person (a GM-like person) to manage the proceedings and take scrupulous notes to compare the two sessions and deal out Slippage. I want to avoid it, but I don't know if I can.