NYC Homebirth Insurance Won't Cover

I am a FTM, 32 weeks, and planning a homebirth. I have UnitedHealthCare through my place of work. I have been trying to get approval for a gap exception for my homebirth for months, working through a biller. We were denied again recently because "there are midwives in network and the midwife you chose is out of network". No homebirth midwives in NYC are in-network, and I have tried to call UHC to explain but they just don't care and won't budge. I call them constantly and I am so tired of this bullshit. In NYS there is a law that all births must be covered by insurance, so am I supposed to get a lawyer and take them to court?

I feel that this is going to negatively impact my birth because I will be liable to pay thousands of dollars for a homebirth. I can't afford that. The biller had said when we first started working together (15 weeks pregnant at that point), that she is sure it would be covered. I was surprised she was basically guaranteeing there would be some coverage. As of now there is none. Has anyone been in this situation? Any advice? Losing my mind here...