I really don't know the answer to your question. I remember arriving in the wee hours of the morning (before dawn) and our site was ready. We chose not to attempt to back in (with the diesel truck) at that hour.
If it were me, I'd probably aim for 10:00. If the site is ready, you're good to go. If it isn't ready, the fort will be wide awake and you could park and explore around the fort.
Regardless, have a magical time!