Best time to enter the park in early September?

Specifically on a Thursday, even more specifically, September 10th. I’ve got a couple off days on tour with my band and we happen to be driving right through Moab, so we’ll be staying in Moab for 2-3 nights. I’m assuming this is a pretty damn busy time of year for the park. The tour is pretty rough as far as driving/sleeping up until this point so very early entry is probably not possible for us. I’m wondering if it would be better to wait until a little later in the day, as much as I want to spend a whole day in the park..