"Can anyone think of a spot that might be dryer, or more windy?"
Humphreys Basin, I'm thinking Desolation/Mesa/Tomahawk Lakes, is up on a high, often windy plateau at ~11,500' or so. There are broad flat areas above all 3 where you could camp away from water but with easy access. You could also drop down and fish Paiute Creek and Golden Trout Lakes from a camp up there. You'd want to call White Mtn Ranger Station in Bishop to check on snow levels first, though. It's about 8 miles from the trailhead to Desolation Lake, BTW, with a total elevation gain of ~2100-2200' from TH. One additional consideration: The TH is at 9400' and Paiute Pass is 11,450', which means that, although the gain is only 2000', you are starting at 9400'. If anyone in your party has trouble with altitude, a day of acclimatization might be in order.