What's the earliest this route can conceivably be done? I imagine that August is ideal, but I might be moving back east and want to get on this before I go. How much snow would there be in late June?
The snow can add ease the hike. Better foot & hand holds when you can kick them where you want them. I've made some assents in snow that would normally not go without technical gear.
The snow drifts on your way up would be of more concern I believe. Ridges and peaks are wind blown are and provide firm footing.