It's possible your board is being discouraging
because they are only thinking about one thing --
money!

There are a great deal of "hidden expenses" in
attempting what you're proposing. Things such as
insurance issues, security issues (keeping the
museum open past regular business hours -- must
we pay a custodian overtime?), administrative
issues (box office reservations, collecting tickets,
concessions, etc) even the expense of additional
electricity to run lights and sound for those nights are
only a fraction of what that $50.00 fee must cover.

And even though you are presently employed by the
museum in your current position (living tours),
creating a theatrical company operating at other
times means you will be considered a separate
entity, working for yourselves.

If you can come up with a plan that will somehow
convince the board that all these expenses that
come up will be somehow absorbed by your
theatrical company rather than the museum, I'm sure
they'll be much more agreeable.

As for there being no interest in the community or
from tourists -- that's impossible to say until it's been
attempted, isn't it?

Best of luck!

If you're going to start a theatre company, look at shows that are definite "bums on seats" shows but that also are practical to perform. Shows about famous people (e.g. Shadowlands, about C.S. Lewis) or based on novels (particularly well-known children's novels, e.g. The Wind in the Willows, The Lion, the Witch and the Wardrobe, The Hobbit) or plays that are in general very famous (e.g. Shakespeare plays) will all attract a wide audience.