Something that could be a solution would be "decider games". These are already used sometimes when a stalemate is reached, ie. the players agree to play another game to decide the winner for both games.
If something like this was implemented as part of the site, it would also eliminate the possibility of some player cheating, ie. not following through with the agreement.
In practice, it'd work like this - when a game goes over a certain round limit, the players are given the option to play another game to decide the outcome for both. All the remaining players would have to agree to it. When the decider game would start, the old game would be put on hold, ie. it'd no longer be playable, and it would not count towards the 4 game limit of freemiums. Whoever wins the decider game, would win both of the games and gain points from both. Alternatively, it could be made so that the decider game is pointless, and the winner only gets the points of the first game. Either way, the decider game option could only be used once, ie. if the decider game also goes to stalemate, you couldn't play another decider game. This could be avoided by choosing escalating for the decider game, as is already commonly done in the situation.