Ash's solution is fine for finishing things off, and is basically what I said about escalation. Directing it at the PC most likely to succeed I might querie, but if it works for Ash then that's worth knowing.
My problem isn't really a defined one but is rather trying to project extended contests on to real world type situations (not for a "realworld" game) as a way of feeling around the topic. Take an election or a football (round ball) match, the official (say narrative) end of the contest may not coincide with the dramatic (negative AP) end.
Of course you can model it with a flexible attitude to the passage of time, say in footie the first two rounds cover an all-out attack, 2- 0, next round is 83 minutes of closed shop, one round. Then let's say you say there's 4 min of extra time. Now here I just think it could be fun to say, this is your last shot, what are you bidding? Then say you end up everyone one +ve AP but narratively that's the end (or conversely, a series of ritual contests which would best be modelled as different skills, but someone goes to -ve AP in the second round).
Of course that individual example isn't necessarily backed by my modelling the potential outcomes, but the central point, if no-one has a specific mechanic they've used for such things which they can just chuck in and say, "Try that", is can you bring in external narrative-derived constraints which might be a fun element in themselves?
An example could be: You have to hold the trolls off until dawn, you've an hour to go, let's give it five rounds, including incremental augments for the lightening sky, if you're on higher AP by the end, Elmal will have come to the rescue.
Basketball and cricket seem to benefit from this, as did those folk at Minas...umm...Tirith? Hell, it could even make grimly bidding 1AP each round exciting.
Sam.
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