You'll need to provide this board with some protections, too, or no one will serve on it.
If I could suggest, a peer-review board to weed out some of the lawsuits would help, too. If there is accountability and sensible limitations, I think you'll find that docs and hospital admins want to see patients compensated. It was doctors, historically, who started the insurance in their first place. It's the lottery and circus atmospherics that have made all dig in their heels.
Proper stewardship is the answer. The system can no longer support a class of parasites in fabulous luxury.