I've got it!
Frodo tosses the Ring into Mount Doom and it explodes, knocking over the chess board! The game was entirely a distraction meant to keep Sauron occupied while Frodo crept past undetected beneath the board.
I'm thinking I'd rather not have a coin flip at this point. Technically, the worst the baddies could've managed was a coin flip, while the best the goodies could've managed was a coin flip. Two of the players left were guaranteed not to vote for a WW, while the other two had a 50% chance, so if we wanted to be true to the odds the coin would need to land correctly for the good side twice in a row to secure victory.
But rather than do that, I would be content to declare
Mith the victor, as she is the highest ranking chess piece still on the board, and stood no chance of being lynched.
**********
Grey wins...
HoME XVI, Derivative Works, Part C, Werewolf Games, section H-
It was an age of compromise in Middle-Earth. In an event unforseen by even the Valar, good and evil united, and the forces of greyness swept over the lands unchecked, doing deeds of compassion and cruelty far and wide. And Mithalwen beheld all that was done, and saw that it was good- and evil. Then she rejoiced and sang, and the peoples of Middle-Earth heard her voice and its surpassing beauty, and they swore allegiance to her and honored her above all others.