Hi there,
I can confirm it's not a blackout. I've just booked tickets from GVA to IAD for the month of July ... and found availability for every day of the month in coach (nothing much within a two month window for business or first).
However, when I tried booking by phone, they showed 0 availability. (For the outgoing flight, they could give me a GVA-BOD-CDG-IAD, but not a GVA-CDG-IAD ... go figure)
Did you try another route? Maybe search for AMS - SFO and see if there's anything. Or, if you can find CDG - SFO, that could help you lower the cost.
In any case, I don't think any other Skyteam airline will talk to you, as they would not be able to deduct your mileage.
Cheers,
GenevaFlyer