Or could a rump Qing become a Russian vassal instead? If we're aiming for a possible Dayan Mongol state, can they make the Qing as a Mongol vassal instead?
I doubt the Mongols still have that power (IOTL, AFAIK, they didn't really try to intervene in China anyway during the 19th century), and about the Russians: as already said here, Europeans (including prob. the Russians) would prefer to leave control of China as indirect as possible, so while there might be Russian influence in the Imperial Court, a full on Russian vassal? No. Also, while the first foreign permanent embassy in Beijing was, indeed, Russian, I don't think the Russians at that point really have the power to extend so much influence over China. I think it's likely that, if a new dynasty deposes the Qing, the Aisin Gioro clan would run back to Manchuria, and basically be left only with that. Manchuria will, then, become a Russian vassal.