also recreating the feeling of a Regency-era ball, wherein ladies would be seen dancing together [...]. However, you would never see two men of the time dancing together in the ballroom.

There's a point where historical accuracy bumps up against civil rights. Presumably you'd never see a black person dancing with a white person at a Regency-era ball either, but I hope it wouldn't be considered acceptable to impose that restriction at a modern ball for the sake of historical accuracy.