Varying "ossia" labels between different flows

I am using Dorico 5.1 and am creating a score with multiple flows (one for each movement). When including “ossia” staves in 2 different flows, I would like a different staff label on each. I.e. one label (“ossia” – the default) in one movement, and a custom label in the other movement.

There seems to be no way to do this: the manual indicates that the Ossia staff label is set through the Layout Options page, so not per flow. Am I missing something? Any alternatives?

I don’t think you are missing anything.
Perhaps you could use staff text and reposition it in Engrave?

Meaning, to omit the “ossia” default text, and replace it with my own staff/system-attached text with the different labels I want?

Can the former be omitted?

Yes, in Layout Options you can uncheck the show ossia label…