I suggest that you're making this too complicated. My family frequently had dinners with this many people. It got to be routine that the hostess would assign tasks as people arrived in the kitchen if the guest didn't just jump in to doing what obviously needed doing.
I suggest, since this is the first time for you, that you, as you're already doing, write down a list of things to be done. Then when someone asks what they can do assign them one of the tasks. You'll know as time goes by where you need the extra person and when you can just say you have it under control and send them off to the living room.
How many you need for each task depends on who is doing it. You will know when another person would be helpful. And for some things, such as setting up the tables you can have more than you actually need to do the job. One child can put out napkins, another, silverware. etc.
We had "supervisors" too. When there was nothing that needed doing, a person could talk with the person doing the job. Getting dinner on the table is a part of visiting and having fun.
I suggest that you can play it by ear and it'll work out just fine. The moms in the group will know what needs to be done and will most likely just slip into place if you come across as relaxed and willing to let others participate. We never had too many people in the kitchen even tho no on assigned tasks per se.