I think, at this point, we're just going to have to agree to disagree. I am actually somewhat optimistic that America will one day have a universal single-payer healthcare system, but I can see I'm rather unlikely to ever convince you that's a good thing ;)
How about requiring the states to work it out on a state-by-state basis? The feds could set the standards, define the problem, and let some kind of distributed processing system attempt to solve it (instead of a one-size fits all approach that sits in stone and can't easily be changed)
I've always thought that most people aren't very far apart on most issues -- it's just the politics, emotions, and posturing that keeps screwing conversations up (and I speak for myself as much as anybody else)
But yes, agreeing to disagree is probably a good thing to do. :)
What you described is how Canada works. Most people seem to think we have a federal health care system - we do not.
Each province has its own health system, the only federal requirement is that they have peering agreements (so you can travel freely without fear of health care). I've seen cases where people who are hospitalized in more expensive parts of Canada are transferred back to their home province (paid by the health care system of course).
It works remarkably well - and from the few Brits I've seen comment on both, it's likely better than the NHS in Britain, which is the monolithic approach you fear. For one thing, health care management is handled at a much more local level, where individual voting districts actually matter, and coverage levels better suited to the local environmental, cultural, etc, requirements.