... Obviously you guys are the experts, and I don't mean to tread, but can't the linking be stored locally on the client side? It already stores the game data. Perhaps something like this could link a "game_id" to a "chat_id", which could then be pulled out by the Adobe Air Client and forwarded to the servers.
Theoretically, people could use a third party program to create bad data, or attempt to mislink chat logs, but since we have 10 people verifying this link it should be "easy" (for difficult values of easy) to tell if people are cheating the system.
EDIT:
A small file that would human readable be something like:
[LINK_ID]
pregame_chat_id=556324987
game_id=54621357984135497
postgame_chat_id=549876347
As long as 70% of the still pvp.net connected clients agree, you know the linking. Anyone with bad data can be put on a watchlist to see if they are scamming. If you can't get 70% agreement, or more than 50% can't send, you lose the linking as unreliable, and report as such in the tribunal.