Why is that frustrating? Just kill both.
I did a Jainzhu -> Manchu -> Qing game right before the release and I was happy with the Ming alliances because I could use them to lower truce time with Ming so that I could attack them every 5 years and conquer them in like +/- 50 years.
At start of the war, just focus on Korea, get one fort and destroy their army and white peace them, then do your war with Ming, that takes longer because they are big, take 100% warscore (15 years truce) and then attack any ally or tributary of Ming right away to start another war with Ming, normaly if they have rebels, loans, etc, they will just white peace right away, so now you have reset the truce to 5 years only. Do your other war and as soon as possible attack Ming again, and repeat. Ming is on 0 authority forever anyway (with the unguarded frontier) so their troops are irrelevant.