Well I don't know for sure via personal experience since I didn't go through with FFS as I originally had planned, but I can't imagine that FFS letters would need to be terribly different.
Buuuuut as an update from before, I had been misled. They wanted a therapist letter and a letter from a PhD holding shrink to do it. Which you have.
More or less they're looking for "Ainsley might be pursuing a procedure that is unusual in the grand scheme of things but not because she's crazy. She also has gender dysphoria, is transsexual, and this procedure would be of great benefit to my patient."
Best bet is to call up the insurance company and ask. BCBS MA which I have (for now) is actually super helpful in this area.