you could Day hike on your overnight permit.
My understanding is that you cannot day hike on an overnight permit.
As for the day hike starting time, I once picked up a day hike permit and asked if I could start at 10PM instead of midnight. I assured the desk ranger that I would not pass the Whitney Zone sign until midnight. I was told that it would be illegal. The day hike permit is for midnight to midnight and all hikes start at the trailhead. Therefore, you must start the hike at the trailhead no earlier than midnight.
Before someone says you can hike to Lone Pine Lake anytime, I asked about that. The ranger said someone at the lake with a day hike permit would have to return to the trailhead to start their day hike at midnight.
If anyone has better, more recent information, please post it.
