For the record, that solution is incredibly biased towards team entropy, and I vehemently object.
Er ... how is it biased?
Note: I mean vagman's solution, not yours. I think your solution is the best one available.
Forcing the match is unfair because playing the doll basically means we lose, since the dolls basically force desync. So we'd just keep playing until you managed to quanta screw us with discord and earthquake and we lost.
Basing in on hp is also unfair, because our deck is designed to take damage at the beginning and recover it later with bonds, so we'll basically always be at lower hp when the desync occurs.
Basically it just says the entropy autowins.