I have found a TPR itinerary using ITA Matrix that looks appealing, which is a mix of BA and AA flights (DUB-LHR-BOS-LAX-PHX-BOS-LHR-DUB). BA are not accepting calls for new bookings for another month, BA website only accept 6 flights on its multi-city system (with min 120 min transfer times between flights). Should I try calling AA, but if so will I be able to get the required TPs as I would by booking with BA?

Advice re how best to go about booking this itinerary please.