I think Germany was more ready to re-ignite the war than the Allies. If Wilson got even more pissed off at the Paris Peace Treaties, he might have started pulling out American troops early as a way to exact concessions from Britain and France... the Germans, even more angry at a more stringent treaty being drafted out of Versailles, might see this as a great chance to put soldiers back on their borders and declare that if the Allies want to force them into this treaty, they'll have to beat them again. They'd have to do this with a socialist revolt going on behind the ranks, yes, but you might see at least a month of continued warfare.