pedestrian: The leading player can double the effect of a draw, thereby bringing himself closer to winning the match. This can be remedied by not scoring draws at all, and I really can't see any serious drawbacks of this solution.

Wait, you do see that the leading player can double the effect of a draw bringing himself closer to winning the match if there's a double, but you cannot see it's beneficial for the trailing player that draws won't count? If I'm trailing in a match, and the current game is likely to be a draw, there shouldn't be any hesitation to double if that means the game effectively won't count, should there?

Of course, you could do something wild like "In the case of a draw, the person holding the cube scores half the count on the cube, the other player gets 0. If no player holds the cube (no doubling has happened) the score is 0.5-0.5". Which means that a score of "1-0" could mean either win by white, or a draw with white having doubled. Non-sensical if you ask me.