re: California--Central Sierras,Stanislaus National Forest, Emigrant Wilderness

I have been to the Virginia Lakes area, where we camped on private land. I did notice a couple of campgrounds by Mono Lake. They looked decent, but have never stayed there myself. No luck with fishing unfortunately, but I am to blame. I've never been in June, so I can't help with the snow or stream prediction. You're right to have concerns this year though.
You should read Dharma Bums before you go if you haven't yet. An appropriate book for your journey.