Oddly enough, both my summer experiences on the rockpile have been around the Solstice.
Several years ago, the snow was gone from the upper elevations, but there was still some in Tuckerman Ravine. They had just switched back from the Lion's Head winter Route to the Tuckerman Ravine Trail. The Alpine Garden was in bloom, and it was a beautiful swath of color across the mountain. Warm sun, cool air, dry.
This past year, it was like summertime, with no water issues going up the Ammo, and plenty of sun and heat.
So that's my recommendation.