A friend of mine flew much of Kings to LeConte, taking photos along the way. Here's his brief report:
I was on a helicopter flight on Wednesday[6/6] to LeConte Ranger Station for Hazard Tree mitigation and was able to photograph much of the high country conditions. In general, the snow line is at 9,500'-10,000' with patchy snow down to 8,000'. Almost every lake I saw, except for East Lake, was 80-100% frozen. The snow depth was considerable in many of the north facing slopes and canyons with little or no rocks showing. All of the major passes in Kings Canyon were 100% snow except Kearsarge. Elizabeth, Granite, Glen and Mather Passes looked like March or April conditions. The rivers are all running very high and numerous snowbridges are apparent. I took images of the Ranger Stations at LeConte, Bench, Rae Lakes, and Charlotte Lake.
I looked at the photos, it's pretty solid out there. Winter for sure above 10,000 -- or very early spring. Dusy Creek, for instance, is running very high. I would expect severe problems at Evolution Creek, South Fork (below Upper Basin); Wallace Creek; Rock Creek (the log collapsed last year). No way you can get to East Lake across Bubbs at Junction Meadow.
I don't think any of this will be crossable for 3 weeks.
If I can, I'll post a couple of the photos, but transferring them from the NPS Server may be a hassle for me (got to work between two computers...).