I've been living in single-payer Austria for 30 years now. When I left the US the HMO thing was just getting crazy, but I was just out of college and never needed to go to the doctor so I can't remember having really much of any costs.
Fast forward several decades and the wear and tear of doing sports my whole life has its costs as well as the massive benefits.
In the last 5 years. I've had double hernia surgery and two surgeries for a detached retina. My total out-of-pocket expense for those 3 operations was less than € 100. Full price would have been (estimate) € 30000-35000.
Austria has what I think would work in the US. Single-payer healthcare covers all the basics and a lot of nice things like free yearly health checks. However, you can purchase private health insurance so that when you go to the hospital you can (for example) get a single room.
For example, one eye surgery was an emergency and it cost € 39 (I happened across the bill yesterday). The second one was probably the same, but no emergency. I saw down the hall there was a VIP room with only one bed. I asked a doctor what an upgrade would cost and she said I could not do a "room upgrade" I'd have to do the whole surgery privately (i.e. with private insurance or pay the roughly €10000 out of pocket).
I think the "calling your representative" is a good idea, and making single-payer healthcare a litmus test for reps is even better.