I was standing in line to get a permit in August a few years back. The party in front of me asked about an early start and was told they could begin at midnight. I chimed in that it would take an hour or two, depending on your speed, to reach the Whitney Zone sign. So, why not start at 10PM or 11PM. Everybody behind the counter jumped down my throat. They were firm that it was not within regulations.
Again, there are no rangers at the trail head at midnight. We started at 10PM several times because we are slow and wanted to be back well before sunset.