I think I'd mentally underestimated how long a sector LHR-JFK actually is! Given that it's almost 3,500 miles, a mile-based programme like AAdvantage could actually work even given the relatively small class-of-service bonus.

I have a sequence of long flights coming up on AA later this year (BRU-JFK-EZE-JFK-BRU) which will easily qualify me for the Platinum Challenge, so I'll sign up for that.

It's a shame about the BA/AA thing, because I'd hit Gold (ie Emerald) every year in Executive Club based on the way BA gives out tier points, but I'll have to add a significant amount of travel even to hit Platinum (ie Sapphire) on AA.