Directly Uninvolve Employers
There isn't really much of a reason for employees to have to get health insurance from their employer anymore. Everyone in a given state or district is in the same pool and pays rates based on their relative risk, and employers pay a health care tax to help subsidize their employees care. Everyone pays less because the risk is spread over large and representative risk pools. The system becomes much more simple, as the employer "middleman" is no longer necessary. Everything else can stay mostly the same, ranging from the plan options to the states' choice whether to run their systems themselves or let the Federal government run it. Rates go down because the pools are larger, and people find the best coverage for them because it is a clear and simple system and they don't have to worry about losing their coverage if they switch jobs or lose their job.