Swiss air will ask you to speak swiss german...
I can tell you, with your experience, and no Swiss "green card" you have no chance in Switzerland.The company is not in a very good shape.
The best for you, stay in USA and have a good life...this is what I would do if I was a US citizen.
(and spend 30-40'000$ in a JAA conversion, would not be very smart if no guaranty of employment.)