If a museum has a board elected by members, and the people elected aren't
of the quality needed, there may be a better answer than eliminating the
election process.
In dealing with people who "have always done it that way," it's sometimes
better to move slowly.

The key is usually the board leadership that is in place -- if it can't
lead the nominating committee (read: railroad) into putting up the best
possible people, then you are actually talking about getting rid of
leadership!

Perhaps the bylaws could be changed to permit a dual system -- i.e., that
half the board seats are elected by members, the other half appointed <by
whom?>