I'm not an expert on it, but I believe that in order to even gain entry to the BA Executive Club you need to fly some high fare segments on BA first...

My gut feeling is probably to go for American, but even there you no longer have the possibility of a Platinum Challenge (which would have been the obvious answer last year) since those now can only be completed on AA metal. You can keep American miles alive with one activity (say a hotel) every 3 years and there's even the small possibility of getting to lifetime status (albeit with 100+ trips like this one).