I am in similar situation, and rather than figure out how to get CK invitation, I decided to get 1K status on UA and simply maintain EXP on AA. I am getting used to it quickly as there are many times I connect to fly AA when I can fly direct on UA. In the end, I fly enough and spend enough to get status on both so hopefully it will mean less time on the road due to less connections. Also, I don't necessarily have to justify paying more for an AA flight when there is a UA flight that is less.