Or to generalize upon my previous idea…
After playing each move, black may choose to immediately take a shot of liquor, which will force white to skip their next turn.
Another way to change the balance in a game is to combine it with another game/sport, for example…
Edit:
Perhaps we could combine Go with darts. As a handicap, White has to throw darts at a paper copy of the board on a wall in order to play their moves. Or maybe both players have to play by throwing darts, or maybe it is something that Black can force White to perform by taking a shot.
Maybe we should just start a new topic: Go Drinking Games!