Don't forget as a AA plat you get BA lounges while in UK for next year on any fare on BA. BA lounges in T5 (and old ones in T4 were great for rest).
Similarly, look at Asiana and see if your rtw ticket accrues miles on that airline to count for Gold Status; that will get you lounge access for 4 years. The BMI lounge in LHR was great!
Whatever you do don't go for FB or skyteam.
My vote is for AA is going in Y, BA if in C rtw.