It looks like recreation.gov is now adding the walk-in quota permits in a rolling fashion 15 days ahead. So today being the 3rd the walk-ins showed up for the 18th. I deduced this by looking at George Creek permit reservations (a "class 11" bushwhack to the second highest CA summit and legally dog-able) which usually has no takers (5 reservations and 3 walk-ins). So if they open the Whitney Zone on July 1, then Whitney via the Mountaineering Route (North Fork Lone Pine Creek) legitimate permits may pop up starting around the 15th Of June in a rolling fashion.