I don't think military medical coverage really counts as single payer; it's an in-house employer plan, it's just that the employer is the federal government. Just because the federal government is paying for it, doesn't make it single payer.

Re: medicare, I think a reasonable way towards universal single payer (or whatever you call medicare advantage plans, as a sibling notes) would be to drop the eligibility age over many years, and eventually get full coverage; and at the same time, add all kids to medicaid. Ex: years 1-10, reduce medicare eligibity age by 1, have medicaid cover kids less than year number; after ten years, medicare covers you at 55, medicaid covers kids less than 10. Years 11-20, reduce medicare eligibity age by 2, still increase kids by one year per year; after twenty years, medicare covers you at 35, and medicaid covers until 18. Years 21-28?, add medicare one year from both ends, and I think at year 28, everyone is covered. Congress should adjust the rollout schedule regularly, as scaling problems emerge, or don't; if after a couple years it becomes obvious that it's too slow or too fast, it can be adjusted; it'd also work, but be more complicated, to do it on a % basis --- once a year, determine what age (years + months even?) would result in a 1% enrollment increase, and do that, you'll finish before 100 years, but I'm not doing the math to figure out how much sooner.