So put this one in the rumor category for now because it's not a done deal as of yet. However, with three separate sources reporting the same negotiations to me, I'm certain things are being worked on, whether they come to fruition or not.
What I've been informed of is that Disney is interested in getting away from the polarization inherent in Hall of Presidents as it currently is formatted. They're also interested in not spending large sums each time a new president is elected. Therefore Disney has reached out and is in talks with Lin Manuel Miranda and Weird Al Yankovic to write and direct a new Hall of Presidents theater show that would be non partisan and more timeless. This would not be a direct import of Hamilton, but might feature some influence. I have no info whatsoever about the animatronics or the costumes, but I can't fathom Disney discarding them. I'm told the vision of the show is "historical but witty".
While I've been somewhat displeased with Disney as of late, I have to say this rumor could actually turn out well. If they can thread the needle of being humorous, witty, historical, and interesting, all while not being offensive, I'm all for it. Weird Al potentially being involved took me seriously by surprise, but I could see this working in a zany way.