I've noticed the lack of category for this sort of location too. I think that you will need to refine what you are asking for, though.
There are sites as you described ... original, restored or reconstructed (often completely fabricated) "Living History Museums" that interpret life in the 1st person (pretending to be from that time period) or 3rd person (dressing and doing activities from that time, but not pretending to BE from that time). Locations for this category would probably have an educational mission and have a 501 (c)3 nonprofit status. Sites in this category would include Colonial Williamsburg, Mystic Seaport, etc.
Take a look at the website for the Association of Living History, Farming, and Agricultural Museums, www.alhfam.org. I think this is what you're proposing, right?
What you want to do is make sure that you aren't opening the gates for any old collection of buildings, working farms, or Historic districts. Half of Amish Country could fit here too. These are locations that have lots of old, original buildings but they have not been designated for educational purposes. This might included ghost towns (with no commercial development), West Alexandria, The Boston Commons, NO's French Quarter, etc.