Well, I took a few minutes to photograph the relevant letters, and emailed them off to Lambda Legal.
Basically the Dept. of State seems to be sticking to its guns; their request of me is exactly in line with their ineffectual arguments in Zzyym v. Tillerson.
With one twist: that "established medical" bit, in my case. Which obvs is bunkum.
Anyway, hopefully in a couple days I'll get some suggestions. Better yet, get added to the existing and directly related case.
(An enby can hope, can't ze?)