How would a no fault scheme work in this context? Honest question, not a loaded one. Would it include tort reform limiting malpractice awards?

"Accident" is defined, including medical misadventure but *not* negligence. Because you can still sue for negligence, its definition is made very precise to avoid legal weaseling. Reasonable compensation levels are then set by stakeholders, including potential beneficiaries- including (say) up to x% of prior salary if you can't work because of injury, a lump sum of $y for loss of a finger, $z for loss of an eye. The scheme funds itself with premiums set using standard insurance algorithms to predict and cover costs. Legislation is probably needed to prevent weaseling to regain the lawyer bonanza environment. Unless you also have a publicly funded healthcare scheme or compulsory healthcare insurance, people will look for ways to disguise all illness as "accident" so you'll need a police force (or a publicly funded healthcare scheme ;-) )

It's not perfect, but it simplifies relationships between providers and customers and limits the perverse disincentives and costs required to feed the additional layers of process that have nothing to do with care.