OTOH you might think about buying one of your transatlantics on AA at a slightly higher fare, set up a Platinum Challenge and go for status, even if OW isn't your main squeeze. You'd get miles on BA inside Europe, even on a couple of BA/AA US-UK codeshares I think (ORD-MAN being one that I believe is exempt from the "no transatlantic credit" rule) and you'd also get access to numerous OW lounges as a Sapphire. Getting 10,000 q-points traveling transatlantic isn't that big a stretch, depending on where in the US you visit.