I don't think that nh reddit is qualified to answer the question. Your best bet would be to contact one of the transgender support groups in the area, such as: https://www.dartmouth-hitchcock.org/transgender-health-program/patient-support-education

What I can tell you is that Nh medicaid (and nh human services in general) is notoriously cheap. NH negotiates fees ahead of time with the medical community, and not all doctors accept Medicaid because of this.

Good luck with your search.