British Airways giving a runaround for involuntary downgrade

I booked a flight operated by American Airlines from DAL to PIT using Avios. I booked a business class flight and BA deducted the points at that tier.

Because the plane that operated that flight was affected by weather earlier in the day, the flight ended up being cancelled. Thankfully, I was at the airport and AA moved me to an earlier flight automatically. Sadly, by this time, there were no seats in my class, so I was rebooked in economy (an involuntary downgrade).

I called American that night and they assured me they would take care of it, and they gave me a link to do request the refund. Sadly, because it was booked through BA, the web form was non-viable, so I went instead to BA to request the refund, which generated case 12391879.

Since then, they've been giving me the run-around. They said that because AA operated the flight, AA was responsible for any refunds or compensation. When I reached out to AA, they said because I booked the flight through BA, only they could offer refunds or compensation.

When I went back to BA with this information, they ignored me.

So I called their number, waited on hold, and spoke to a person who said they cannot help with "customer relations" issues over the phone, that I must do it through email, but that they've updated the email chain and I should get a response. I did not get a response.

On 07-05, I sent another email to the case indicating that I'm still experiencing the issue, but I received no response.

On 07-08, I called again. The agent apologized, but mentioned there was nothing he could do because the global relations team only operates in India Standard Time (approx 07:00-17:00 IST), so I would need to call back during those hours. But also, the hours for calling customer service in the US are only until 23:00 (or maybe 01:00?), so I would need to call between the hours of 22:00 and 23:00 to overlap with the "global customer service" team.

Seriously, who designs a call system where the overlap of the incoming calls and the people needed to service those calls is one hour per day? It's a company who doesn't care about customer service.

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