Jonathan, I think that is what Hobbes is looking at. And why not? If the permit is for a Friday start date, there is no rule saying you cannot start your hike at 9 PM. That is what I did on the Shepherd Pass trail one year. (Hobbes, getting over Shepherd by 9 AM would have required me hiking ALL night!! grin  )

Inyo has mostly been talking about Night Box pickup enabling people to drive in after closing, get their permit and start really early next morning. But actually, the Night Box pickup for an evening start should work, too. I think you would need to stress to the people working the night box that you plan to pick it up that evening, or they might remove it, thinking you are a no-show.