You should easily be able to sue BA in NYC but would have to leave how to do that to others. BA has terrible after sales service even if you have BA status but GGL can offset this a little.

I would not settle for this personally, as you recount events BA has treated you very badly. If you can sue them as easily in the US as a small claim in the UK this is a mechanism to force BA to look at the whole thing properly rather than dealing with poorly informed call centre staff. That is what I would do in your situation.