And quickly, too. It seems that reading the Help that comes with the board game thing actually helps, as it tells you that a fight that results in a draw means the opposing side can’t move. With this, I used The Cheat to prevent Strong Mad from moving, Homsar to ground Strong Sad, Coach Z to distract Homestar, and The Poopsmith to hide The King of Town every move.
In 9 moves, I’d won both the battle, and the game. Hurrah!