Pro tip indeed!

AA shows 1st Cabin availability from BKK to LHR (1st cabin for first leg via DOH, biz class via second leg, which departs a day later). This doesn't show via BA directly, however yes, if I search the individual routes they do indeed show! Not sure if it's the class mismatch or the 2nd leg departing a day later that's causing the issue but seems like availability is indeed there! Much appreciated for the support, I'll give BA a call now. Thank you all!