As a fix for the whole draw issue, I propose that you add a Concede option. This would be a cross between Surrender and Draw, where the ranks are fixed as they are, and the game is ended. The primary difference would be that first place does choose to activate it.
The use here is for either stalemates where one party is vastly larger than the others, or for games where one player has an overwhelming advantage. In a stalemate, the larger player may be unwilling to draw, believing they have an advantage, which while it may be true, would only break the stalemate with very low probability. A Concede button would essentially allow a surrender where you don't feel that you're giving up your position. I'm not sure exactly how exp is calculated, but I think this would fit in with a reasonable system.
The main point of this is that it stops needless waste of time on games that are no longer interesting. It would be quite acceptable to get a bit less experience to end a game that already has a set outcome.