Please see
this thread where a similar discussion is already going on.
In essence: LX has announced about a week ago the schedule which they intend to fly in June, and is in the process of removing all the other flights.
They currently say
on their news page that they will offer in June to the US:
in addition to its three weekly services (from Zurich) to New York / Newark (...), flights from Zurich to New York JFK (4 times weekly), Chicago (twice weekly)
It seems obvious to me that they just used the "quick and dirty" option of setting the availability to zero for many flights which won't operate, and the timetable is not fully cleaned up yet. So I'd agree with you: Those flights with zero availability are not sold out, but they won't operate with a 99% likelyhood. Reservation agents with at least some basic training should also be able to see the load themselves and realise this.
As to your options: I'd definitely stay with Option 1, i.e. wait until your flight is officially cancelled and ask for a refund. Please note that LX takes a looong time to process refunds at the moment. They say that they will pay, and they have a substantial government grant, but they need time.
I see no reason why you would have to accept a rerouting, even less so if you are US citizens and won't be able to enter Switzerland by mid June.
Trying to change non-refundable into refundable via a voucher and a new ticket is not a good idea.