@JLynch, by June 4, there will be a lot of boot tracks heading up the "chute" (slope west of switchbacks) Gaiters are always helpful on such slopes.
Jbyrd, snowshoes are good if you are the first one in following a fresh snowfall. But otherwise, I'd leave them in the car.
AnnieAM: I, too, am curious about the availability of water at Trail Camp. I am hoping someone will walk over to the inlet stream that feeds the Trail Camp pond, and see how accessible water is there. As for switchbacks: The chute is probably easier for now. Watch for reports, though, when people come back saying they used them.
Bobby R: I don't think you need snow shoes. Crampons yes. Be wary of deep snow along the trail from Trail Crest to the summit. Lots of fresh up there, so just hope others have packed a path through it.