I'm pretty sure I ran that in a couple of hours a "few" times, more than a "few" years ago. It will likely be hot and dry by June in any normal water year. This year being ~50% of normal – well. I'd recommend hitting it within a few weeks of the snow level melting past 8000', late "spring" as you have proposed, when surface water, greenery, and wildflowers may be abundant. But hey, it will likely be great, as it is Yosemite after all, ANY time of year, and certainly within your capabilities given your past hikes. For the record, my favorite late afternoon journey (run) was up the 4 Mile Trail and down the Panorama through Illilouette Ck. and down to Happy Isles via Nevada and Vernal Falls, made comfortable anytime the trail was dry, even in the heat of summer, by the shading provided by the route's general northern exposure (i.e., being on the South Rim).