Thank you all for your input and advice.

My TA was not given a reason by BA for declining the OWE fare - it was suggested that perhaps they were being obstructionist as I elected to fly AA LHR-BOS, rather than BA. I find that hard to believe.

All the flights are operated by AA/BA/CX/LA - there are no code shares involved. I think I'll take the advice of bouncing it over to Cathay and see what happens.

Again, thank you all for your help!