My wife and I are in France on a 1-year renewable VLS-TS visa. You can get this by showing proof of income OR savings (we used savings). It was pretty easy, just one 15-minute appointment in Atlanta.
You still would technically not be able to do your remote job. I've known people that did and it wasn't an issue for them.
That's awesome, mind saying a little bit more about your experience? Appalachian trail/PCW? What was your favorite area?