I really hate to be negative, and nitpicky, but if you have to remove every single piece of wood and other material down to the bare frame, and replace it, then you are not really "restoring" the original. You are "rebuilding" the original from new components. Which is still cool, but not at all the same thing. To say "this is the original set/prop used for filming" is not entirely accurate at that point, IMHO.
Having said that, though, I still think it's a cool project, and I wish you well with it.
This is the problem all museum facilities face when considering preservation vs. restoration, very well boiled-down in the "grandfather's axe" aphorism above. My own choice is the real thing, with all its blemishes, as an historic artifact from 1960s Hollywood.