I think what we need for people who don't want insurance is some way to "opt out" of the health care insurance system - maybe a special card you carry that indicates to the emergency room or hospital (where maybe you have been admitted, unconscious and close to death from a car accident) that indicates any medical assistance provided will be 100% your responsibility - i.e. bill me or whatever. 

Why do I need to carry a card? What purpose does the card hold other than to tell the medical provider to treat me differently (as if I could either not pay (unfair to me, how do they know my assets) or could pay for better treatment (unfair to everyone else, why are some suffering through mere insurance while I have the good stuff that daddy greenbacks bring))? If you are differentiating for those without insurance, you surely must do the same for those with the comically legal 60/40 plans that have no practical out of pocket cap. 40% of a 100k bill is practically the same as being uninsured when looking at the effect of causing a bankruptcy to most of the country.

    The only problem is that someone could then just claim bankruptcy and push the burden back onto the insured - so we'd need to make it so bankruptcy could not remove that outstanding debt.

Would you prevent people who signed up for 60/40 co-insurance from Aetna or Blue Cross to file for bankruptcy when they cannot afford to pay their 40%? If not, why? They choose* to not pay for better plans that limit their out of pocket liability.

Making bankruptcy harder isn't the right solution. Complete nationalization is only solution that doesn't leave uninsured and underinsured individuals who need to take a bankruptcy after an illness or accident. If that is truly the goal, then that is what should be worked at.