One alternative is to status match to AA and collect everything their whilst you fly BA - you would need to do the research if that is worth it or not.
Obv. try the status match to BA, but I doubt that works.

One last alternative is flying on star alliance (SAS and Swiss Air come to mind), but that will only get you partial coverage. It does position you well to fly out of ORD again on UA if you get a UA status match...