Since US taxes were unescapable, I eventually went for tourist visas, moving every 3 months. The host country does not consider you taxable. I used this in Spain in particular. It worked out fine. I had a spanish lawyer and a spanish accountant, both were of the opinion that it was above board as long as I took longish trips every few months. As long as you're still working remotely and not using social benefits, there's no real legal category for you yet.
There is private health insurance explicitly designed for Americans living abroad. It's dramatically better (and cheaper) than regular american health insurance. Mine, for example, was $1700/year for 100% coverage outside the US and an extra $2900/year for 80% coverage if I wanted it active in the US too.