Piggy-backing on that great idea (that has worked for us on several occasions)...sometimes you can make a reservation for a smaller group size and just tell them at the counter that your party got larger (or call ahead if you're worried.) We had no trouble changing our party size on past trips.
NJGirl and RachelA - thanks for the info...we are not getting in until 5/25 so those dates don't help me. I will keep trying and will try a party of 6 to see if that works (since our 7th person is a toddler).
Have you tried today? I was able to get a lunch ressie for 4 on the 25th and just checked a few minutes ago and there were still more.