Thanks Mullhollander, this is incredibly useful.

ANOBAG seems to be the keyword I wasn't googling yet, and this seems to me the best route.

Seems I just go to Ausgleichskasse and register as a working for a foreign entity with my estimated earnings? Will they explain where and how to pay my AHV and other obligations? I already bought my own accident/liability insurance through the health insurance company.

I guess the Third Pillar is optional, and probably doesn't make a huge difference for me, since I have to pay US taxes on the earnings even if they are in a swiss pension.