It appears possible to have a variable filter that has no moving parts. It is done with liquid crystals and commands over an rs232 cable:

http://www.dfisica.ubi.pt/~hgil/fotometria/cri/varispec2.pdf

The specs show that you can have a selectable filter from the blue into the NIR – but not in one device. The stability of the ability to dial up a specific filter needs to be investigated. Papers have used this device, such as this one.

The transmittance is low compared to glass, but with a moon that bright, who cares!!!

Scattered light in the filter could be an issue.

Highly sensitive to polarisation — one could make that a feature?

Filter stability would be the other issue — would they change transmission characteristics on long term (year) time scales?

Chris comments:

the transmittance is low compared to glass, but with a
moon that bright, who cares!!!

scattered light in the filter could be an issue.

highly sensitive to polarisation I see — one could make
that a feature?

filter stability would be the other issue — would they
change transmission characteristics on long term (year) time scales?

infrared and optical handled differently, so two would be
needed — could lead to calibration issues…