I’m thinking the way to go is concierege with a mutual insurance co. set up to lay off accidental injury.
I doubt that the second part is legal. The government would call it medical insurance, and every state would have to approve it separately.
On the other hand, there would be a market for a concierge medicine exchange, or a cash doc exchange. It would beat Craigslist or word of mouth. Any database guys want to try it?