IVF Insurance Billing - Bundled/flat rate service fee?

Has anyone ever had to deal with their IVF cycle being billed to insurance as a "bundle?"..meaning they bill as a flat rate to the insurance company? My provider says they are required to bill a $10,500 flat fee for the full IVF cycle INCLUDING labs and monitoring. I have a $10,000 infertility benefit limit on my insurance so this is a problem because my insurance says normally the labs and monitoring (about $4,000 worth) would be covered under my regular medical coverage, but now it's being applied to my infertility benefit, leaving me with a much bigger out of pocket cost.

I'm already midway through my cycle and just found this out and found out also that NY State is implementing a law that requires my insurance to cover 3 cycles in full starting Jan 1 ...bummed I didn't find out about this earlier, otherwise I would have waited!

Wondering if anyone has dealt with the flat fee billing and IVF limits and has successfully been able to work around it?