I also had similar problems with agents saying such things as "there aren't any availabilities till ### month" without even trying to look for seats.

Another data point. I was able to get my seats to Europe on LX from JFK to BEG via ZRH in early September in F. I don't know if it's because this is a US to N.Asia via Europe award, but it seemed like there are availabilities to Europe early September in all classes.

August may be a different story, but I'd figure that things are better in late August.