Keep checking the online reservations system. I got lucky a few days ago, and snagged a Saturday night Chef Mickey ressie at 5:30 for my trip in 2 weeks.
Keep an eye on the November Cancelled ADR thread to see if anyone cancels a reservation that would work for you and your family.
When you have a chance, please read the first thread of that thread or the sticky at the top of the forum that has the policy on cancelled/wanted/trade ADRs.