I cannot answer all of the intricate timing about the chute (many others have recently been up there, so they will weigh in, or you can ask around at the Portal)
However, I urge you to place SLEEP as your number one priority (it is only wnen you sleep that you are truly acclimatizing efficiently)Taking an informal survey of sad-looking hikers on the switchbacks, with confidence, I would say that the statistics showed that those who started too early were the most exhausted by mid-day -- no matter what shape they were in (too early would be a start without adequate sleep -- not necessarily based on wake-up time, itself).