Is PDX to Greece for 4 realistic with points during school breaks?

Pointify is tracking this award space for the points-and-miles community.

My wife would really like to go to Greece, and I've been trying to figure out whether award travel is realistic for us. So far, every promising option I find seems to end with "no award availability," during the dates we're able to travel. There are 4 of us total, 2 adults and 2 kids. Our home airport is PDX, although we could potentially drive to SEA if it made a substantial difference. We would probably travel either during spring brea