"I think getting doctors on a salary is the very first solution..."The original rationale for HMOs was that the insurance company would be paid a fixed amount per patient per month (although this might be modified by the patient's pre-existing medical conditions) and would be required to provide whatever medical care was necessary; therefore, they would have an incentive to do things the most economical way, i.e. through preventive medicine whenever possible.
That sounded great to me, and it still sounds like a good goal.
Unfortunately, as Adam Smith predicted (when talking about education), instead this gave an incentive for insurers to provide as little care as possible, by making the quality as low as possible, and making it as difficult as possible to obtain it.
In Bryan Caplan's class on microeconomics, he explained the concept of "moral hazard" to us, with plenty of amusing examples. I suggest this as another one.
So, how do we actually accomplish the original goal?