Larger parties can be tough...Have you tried booking lunch instead? I just booked my trip and all ADRs for end of Aug/begining of Sept. yesterday and got Le Cellier lunch at noon on 9/3. Here's some pixie dust!
Or - I saw this suggestion on a similar thread, yesterday - make two reservations. One for four and one for two, or two for three people each. Check in early and offer to wait for a larger table or for two tables next to each other.