Companies have leverage due to size that individuals do not. Private insurance for worse coverage than I have now (and mine is good) is almost 2x what I and my employer pay.
So why can't you and a thousand of your closest friends get together and organise private health insurance for you as a collective? Then you get the size leverage. You would also be able to pay off the risks that one person might face, because although some of you will have high health care demands, chances are some of you won't. Isn't that how it's supposed to work? By competition, arbitrarge, etc?