happened to use the word rota the other day, only to find that my interlocutor (a USn) had only the
vaguest idea of what I meant

I don't have even that.
Just the title of the tread let me add that the Italian word ruota (rota in some dialects, and in an archaic form) means wheel.
A related meaning was about a rotating device used in convents to connect the inside part with the rest of the world without seeing it, for example to receive food. It was used also to leave there the unwanted children.