Wow, what a great idea. Let me be the first one to sign up!
Based on your calculations, the 60,000 proud owners of the mansion should have an equal share, making this the most luxurious time share in history.
The administrator (you, since this is your idea) would have to keep track of all scheduling issues. To keep things manageable (and to avoid neighborhood scrutiny, as well as police and fire department closures), I would suggest dividing up the property into 365 time shares to be shared by 164.38 people.
While sleeping arrangements might be cramped, 13.69 people sharing each of the twelves bathrooms is a far better arrangement than one would find at football games or outdoor concerts.
Each group of 164.38 people would appoint their own leader to manage time share activities (parties, meals, sleeping arrangements and clean up) and pledge their group to do one hour of chores during their day, which would eliminate monthly maintenance and repair expenses. Imagine, for example, what 164.38 people could do in one hour of gardening!
[UPDATE] Okay, I just watched the video tour of the property and it doesn’t even have a pool, tennis court, or in-home theater.