Just based on what you say, it seems the therapist is following his training and protocols, and the lack of experience is driving the decisions. If you are getting insurance coverage for your issues, then it may be GID isn't covered or isn't covered as a primary condition. Most therapy programs, especially those covered by some insurance, requires a diagnosis, a treatment plan and a limited full-coverage number of sessions (often twice a month plus a few emergencies per year with a limit in years).
I am surprised if he is a transman and working in LGB"T" issuses, he doesn't know the process and work. He has his own experience to work from and likely knows other transpeople to help.
Do you have primary care physician? If so, the therapist can write the letter to them and they can, if they don't do the necessary blood work in-house, refer you to an endochronologist. Otherwise, it seems reasonable to me the therapist write a specific letter. I don't know of any who write generic "To who it may concern" letters for hrt. This doesn't stop you from finding a endochronologist and discussing your interests and asking them about the letter.
As for the SO, it may be the lack of exerience or interest. Finding another therapist is your choice, but it's worth exploring if you're uncomfortable with your current one to find a new one. Remember if you do, you have the responsbility to inform the old one if you want him to forward any information or records.
Just my thoughts. Good luck.
--Susan--