Someone who bills himself as "Trevor the Games Man" wrote to me about something that isn't really worth it lot of discussion so of course we're going to discuss it…
I'm a full-time entertainer. A gender-neutral word for "showmanship" is "stage presence", as in "That performer has such excellent stage presence: they had the audience in the palm of their hand the entire show."
I dunno, Trevor the Games Man, I always thought the word "showmanship" applied to a person who put on the show even if they themselves did not perform. In the case of your shows, I suspect you do both. "Stage Presence" is what an individual performer or act brings to the proceedings. My friend, the late Max Maven, used to define it, at least with with regards to magicians, as "Establishing a rapport with the audience that makes them eager to follow you wherever you take them."
Which I guess is the same as your definition. I still think I need a word to describe the quality a lady would be demonstrating if she assembled but did not appear in a great show.