As the OP is flying 90% to China & Japan, to use BA would add at least 4 hours to the journey and the risk of getting stuck in LHR. I think BA is only worth it if they fly direct to a destination that is not available from Frankfurt (Chengdu?).

However there are plenty of airlines flying eastward from FRA to Asia/Japan and I would recommend the OP try them (including the ME3). If in C or F, I'm not sure status makes that much difference in the air. Maybe you would learn to love [the IMO not exciting but consistent] LH service again!