Draw up a contract whereby you are only obligated to pay the doctor while healthy. The doctor loses money as long as your health is suboptimal and therefore it is in the greedy doctor's best interest to do everything they can to keep you healthy.
The same approach can be applied to any service that requires regular intervention to avoid service interruption. If you pay someone every time the service is interrupted, then they’ll be incentivized to do a bad job so it gets interrupted more frequently (e.g. contractors tasked with ensuring traffic lights or electricity supply works all year round in all weather conditions).
Pay a flat rate for continual service. Beyond a certain reasonable/acceptable level of interruption, reduce what you pay them. Eventually if they do enough poor quality work they’ll go out of business - as opposed to the current conventional approach that incentivizes them to do poor quality work.
If this applied to certain goods as well (like electronics) we’d probably be able to get rid of planned obsolescence.
Also, what happens when people self-select such that only people who often get sick take on these contracts, and people who are normally healthy stick with pay-for-service?
Only if they cannot help you. In which case you have the same medical outcome but save your cash.
Doctor locks up money under contractual obligation. If they act dishonestly and your health declines, they lose their stake.
As long as they act honestly, they are rewarded.