Things are pretty heavily snowed here, especially the peask farther to the north. I climbed La Plata (practically right next to Elbert) last week on May 15 and it was almost all snow from the trailhead at 10,100'. Some of it is pretty deep too, and on a warm day the wallowing gets pretty ridiculous, but can be mitigated some with snowshoes. I imagine Elbert is holding a lot of snow in the trees too, and I can see the upper route from driving through Leadville the last couple of weeks and its got a lot of snow up there too still.
Its hard to say what June 15 will be like, but I would imagine that this year Mid-June is going to require snowshoes, waterproof boots, and tall (knee high) gaitors. Should be soft enough and the ridge is gentle enough to not need ice axe or crampons though, usually don't need them on Elbert anyway.
Can't answer to the Front Range as I haven't been by it in a while, but last I heard Torreys and Grays trailhead was undriveable, you can only get maybe 1/2 mile above I-70 before its snow covered the whole way.