FYI, I just spoke with the Wilderness Permit Office to try and nail down permits for 7/15. No luck yet, but Jessica mentioned that they have availability for July 4, 5, 6 & 7. The website shows only day permit availability for 7/7 (3 of them). I believe they're somewhat slow in updating their website numbers.
Wanted to pass this along in case anyone is mulling a holiday week climb of Whitney. I failed to ask her whether they were day or overnight.