Pragmatically speaking I have a few thoughts that would generally improve things without raising spending, and decreasing government red tape...
1. I would like to see the spending the government currently does regarding healthcare (govt employees, elected officials, medicare, medicaid, va, etc) rolled into a non-profit healthcare corporation. It's important to include the government officials and staffing here, as they get the same as everyone else to discourage tiered services.
2. From there, I would make it a requirement that Insurance Corporations act and negotiate as a fiduciary on behalf of their clients. One of the serious lapses in the Obamacare legislation that has let insurance companies largely not try to negotiate prices down in order to raise the oceans in terms of costs/profits.
3. I would seriously reform/eliminate extension patents. (competition)
4. I would make dual-sourcing a licensing requirement from the FDA. (security + competition)
5. I would make 50% US production for all medications a requirement for FDA approved use (security).
6. Any company can purchase coverage policies from the Non-profit insurance corp that covers govt employees and current welfare coverage programs.
7. Require no more than a 20% pricing variance between customers in a 15 month window for a given procedure by a medical provider. (no dual-books for insurance covered and private pay)
While there are other steps that can be done... part of it is to merge and adjust spending directly based on current spending, but having a non-profit corp that also covers govt employees is a baseline. By breaking it off, you can allow for a stronger level of competition of services.
Reducing patent protections, and making dual sourcing and partial domestic production requirements you again encourage competition. The requirement for dual-sourcing is partly security and partly to ensure competition.
Now, this is emphatically not a Libertarian ideal, and would not cover everyone, but what it would do is expand competition and reduce incentives for poor behavior. It should have the side effect of lowered costs over time. From there, individual states could create their own expansions or services beyond this, as could specific cities.
Over time, I'd prefer to see the FDA shrunk and sane guidelines in their place... Allowing for input based on relatively trusted testing to allow/disallow certain medications and reduce the incentives to produce less-good drugs only to expand patent exclusivity.