Craig, I don't want to be the bearer of bad news, but the permits from Yosemite, ( Happy Isles and Lyell Canyon ), are booked solid from early June to 24 weeks from today. You can check on trailhead availability on the Yosemite website. The good news, is there is a 'work around' if you are willing to do a slight detour at the Happy Isles TH. You can get your permit from Happy Isles to Illouette Falls, then backtrack the 3 miles to the JMT junction and on your way. The permit rangers get a 'snitty' with this method, but it is legal and there are usually spots left for that option. You start at Happy Isles, hike to the top of Nevada Falls, then head to Illouette Falls. The next day you would have to double back to the JMT. You can take your chances on a walk-up, but be willing to wait in a long line the night before the permit station opens. I will be doing about the same pace as yourself, only leaving in mid-August. If you have any questions on this slight route change, you can PM me for more info.
There will be trails cut on all of the high passes from the PCT hikers by then, but with our snow this year you will have some snow travel, particularly around Muir Pass.