Calicokat: Thanks SO MUCH for the pictures! I posted several of them and a link in the Current Conditions thread.
People really need to see these. It shows how tenuous conditions are. When it is icy, one slip could be the last. But during mid-day when the snow is softer, it is so much easier.
There will likely only be patches by late June. I would expect you will be able to hike the switchbacks without touching snow, and only the patch below the summit hut will be there, with a deep groove through it where all the hikers tread.