My last trip was on June 20 of an average year. Most of The 97 were buried under several feet, and nobody was on them. The clear route was up the snowfield directly below T-Cr with crampons and ice axe. Switching back until the crust softened, then straight up cut steps. That was only 10 days earlier than you are going and in an average year.
(Ah the good old days. There were exactly 4 parties above Trail Camp by 6 AM that day, and the only guy ahead of me was headed for Muir first, so I had the incredible experience of having the summit all to myself for about 1/2 hour on a warm, perfectly clear morning within hours of the solstice. A Sunday, no less. But I digress.)
Beta may differ come June, but I would be prepared with spikes and axe. Given this years snow pack, I am packing them to California mid July, and will decide whether to carry them in after I get there.
