The principle is to pay your own medical bills out of an accruing investment of ownership in healthcare/insurance company that also provides fair cost protection.
Lets create a company, a fund, or even a cryptocurrency. Instead of paying for insurance, you buy stake, stock or coins in a general fund. This fund is controlled by a kind of governance system and every contributor has voting rights.
Every member can contribute as much or little as they wish, from which amount they pay for minor/basic health care benefits. One can also loan or borrow according to special rules. This way, you can pay for yourself and in case of having too little you can borrow it. In case of a catastrophic injury or disease, a small regular insurance payment can protect you.
If high-costing care is simply a given for you, then you should buy more of this ‘care company’. Think of it like a retirement investment, allowing you to prepare directly for future health issues. At any time, company investment can be sold.
This company would have its own insurance specialists, whose main purpose is to determine if prices are fair. But to simplify things, the care company could own its own systems of health treatment. Like Kaiser they could have doctors, nurses and facilities which accept payment from the fund.
It could rent out rooms in hospitals, hire staff and own buildings where many members/owners live. If necessary they could create mini-hospitals. It could also have a legal division protecting members getting care and medical staff.
It could contract out or handle catastrophic insurance for members. Hopefully this would be very small in cost, covering only unlikely events. If costly health issues are likely, one should buy more funds/stake or prepare to borrow.
For those without insurance, government could require that free health service incur borrowings in such a system with a promise to pay for bankruptcy/unpaid situations. That way, a poor person needing help would still have insurance-specialist protection, a debt to pay and government intervention as a last resort.
Conclusion
The basic principle is that you pay for whatever you use. Isn't that more fair and much simpler for determining such subjective things. Also, all money paid is an investment. Vertical integration helps prevent unknown or uncontrolled costs. This could be fairer and much cheaper.