Balance billing for in-network care under gap exception?

My insurance company granted a gap exception for an out-of-network provider, acknowledging that their network didn’t include providers who offer the specific kind of care I need. (Additional context in my original post.)

My in-network copay for this kind of care is $20. My provider charges $475. I pay my provider directly, and then I get reimbursed by my insurance.

My insurance company is claiming that they’re responsible for only the $200 “allowed” amount and that I need to pay the difference. I’m arguing that, since my insurance has agreed to cover this as in-network care, my cost-sharing should be just the $20 copay. My insurance is telling me to negotiate directly with my provider or to find an in-network provider…which I can’t, which is why they granted the gap exception. I told them that they’re responsible for negotiating a different rate with my provider if they want to, as they would be for any other in-network provider.

Anything else I can try? If they reject this and expect me to pay the full $275 difference, I can’t keep seeing this provider.

I’m a 31-year-old woman in New York, with Blue Cross of California coverage via a self-funded plan through my employer. Thanks in advance for any help!