If I were the one making the decision, I'd change American healthcare with one big thing, modeled on the Japanese system... price controls. Japan's system is more or less like ours, but with one key difference - a government panel sets the prices for all medical goods and services. Providers and insurers have to make their profits within that price structure. This incentivizes both to reduce costs, for the sake of their own profits.
Of course, this would be called radical socialism or some such stupid in America, and Democrats aren't even talking about it (Republicans have no ideas at all on health care). But it's politically a much lower threshold than single-payer (throwing out the whole framework and starting over, basically). And it demonstrably works - Japan's system costs less than half what ours does per capita, with better outcomes.