It's a sensitive topic for him because he knows I want to go on HRT...

How do I make it as easy as possible for him to understand taking me to see a therapist would be a positive thing? He worries they'll be a "gatekeeper" and just prescribe hormones for the sake of money rather than helping me. He worries they'll be unprofessional or unqualified to make any diagnosis because I want to go to a free clinic.

Again, this is a difficult thing to talk to him about... He'll either finally be okay and book an appointment for me after this or I'll have to figure something out when I turn 18 next year.

The only way I can think of doing this is with the truth. Explain that this has become a huge distraction and you fear it will/is affecting your ability to do school work and other things in your life. It's possible if nothing is close, a Skype therapist would be a good solution and that would be easer to schedule.

I'd be honest and tell him how much you want therapy, how it'll be helpful to you and how much it'll help you with your being trans. Sending him articles about being transgender may also help.