I can only reiterate what KARFA says. It is hard to give much help knowing very little. For instance, you insist on the fact that the flights are BA coded, but that's effectively irrelevant. The first flight was AA operated so the issue seems to have been theirs.

I'm also not entirely clear what specific advice you are asking for. If the worry is about the TPs, then indeed, I think their best bet is to ask for ORC (see relevant thread) but note that it is not a very straightforward process and it doesn't work every time especially in complex situations.