Grand Gatherings are labeled as "experiences" and not all of them include meals.
You might want to talk to Group dining and I would do it before your 180 arrival day mark. I would ask their opinions of how to do this the best way. You will not be allowed to make ADR's until the 180 mark but at least you will have a plan.
The number is 1 407-939-7707. If you call the regular dining number and tell them you want anything over 8 they will most likely transfer you to group dining any way.
As to what is the best way to do it that is up to you.
We are having a family reunion in December and big meals all together have always been a huge part of our celebrations. We do not expect to stay together all day in the parks, there are going to be 17 of us but there are several dinners that are important to us.
My parents will be celebrating their 69th wedding anniversary while we are there.

We do not want to be sitting at many tables all over the restaurant. We want to be together for this one!
I have had a really hard time getting ADR's at the places we want. I even picked the places that I wanted the most and tried to schedule them the most distant from our arrival thinking less people would have booked them but still no luck.
I would say if meals as a group are not important to you then split up and it will be much easier to get ADR's.