While it may be wrong of people to assume that "girl in gentleman's clothes" means just that instead of "gentleman," it's not an unreasonable assumption, especially within the context of a striving-to-be-semi-period-correct 19th century art form. In society at large, cis-women/girls/females/etc. wear masculine clothing without so much as a sideways glance unless it's something elaborate like a tailcoat (and elaborate dress of all kinds gets noticed, so the notice might often be simply because it's unusual, not because it's gender-unusual). Cis-men/boys/males/etc., on the other hand, almost never wear feminine clothing unless it is specifically to play a part (comedy, drag show, etc.). So then the obvious assumption is, "girl in gentleman's clothes" = girl in gentleman's clothes, and "boy in lady's clothes" = boy playing a girl, temporarily. Now of course I'm not saying this is the way it should be, only that it is.

Basically you'll probably need to repeat this line: //In more blunt terms, when I put on the full tailcoat et al, I am not a lady dancing the gentleman's role. I am a goddamned gentleman, and I will dance the gentleman's role, except in the most dire or intriguing circumstances// over and over until they get it and keep it, because it's nonstandard.