Hi Dale-I would think that as a publicly supported institution and museum, they would be obligated to give access to the collections. It would seem that it should be possible to make an appointment well ahead of time and then have the opportunity to see them. If you don't hear or your request is denied, it would be appropriate to go higher (the governors office?) to make your case.
They may be nervous due to the fact that the Haines, other rifles, artifacts and CW swords were systematically stolen some years ago (by a Society employee) who sold them outside, to a friend. Most things were recovered, but probably not all.
This is why I am no big fan of public ownership of sensitive materials such as these, given the huge bias against guns among the cognoscenti of public employment.
Good luck!
Dick