Why do you expect that an itinerary will necessarily cost the same number of miles if you redeem AA miles as it would cost if you redeem BA miles?

Or am I as confused as BingBongBoy about what you mean?

And, for further confusion, did you actually mean that "the snooty CSA on the phone could not care less" - that is to say, that she cared so little about helping you that it was not possible to reduce her level of caring any lower?