Re: American moving to Switzerland
I think you could apply for a residence permit through your girlfriend. Unlike the US many countries in Europe do recognize "cohabitant or living partners". One of my colleagues recently got one for his girlfriend. So I am not making this up.
Your GF has to be able to prove that she earns enough to support you, though (and more importantly convince the canton). As one of the above posts suggests, talking to her company lawyer or whoever is handling her visa would be the best.
Just to warn you that this may not be easy..... he had to go through several months of agony to convince the authorities that she was not a passing fling. And the company officials must be respected in that canton. And they must be willing to sympathize with your girlfriend.
You could do this when you come to Switzerland. It takes time so so this immediately.
All the best.