The first step in the process you're trying to promote depends on breaking the hold of big insurance companies that have their hooks into corrupt politicians.Anytime the government subsidizes something, we get more of it. No system is going to be absolutely good.
So I think the private market, ran by healthcare professionals (and financial people who the MP's choose), would be the best way.
Then ad in just enough government overseeing to help insure the lies and greed are kept to a minimal.
And under no circumstances should the profits of the medical profession be allowed to go to any politicians by ways of MP's lobbying.
In order to break that hold, government reform is obviously required.
Then perhaps your 'health care professionals' could administer a new system, but only under government control that outlaws corruption and payoffs to those professionals.
Who would those 'clean' HC professionals be and where would they come from?
I can't see anything that can eliminate corruption other than the power of the law, and that requires government. Good government works but there is probably no government that is completely free of corrupt politicians.
Don't abandon your idea! Refine it into something that could become remotely possible. The rest of the modern world has only found one answer so far. Albeit with some modifications.