No. You need a super plural here. Y'all is for a group. Multiple people. But you have a grouping of groups. Groups of multiple people.

"All of y'all" is correct.

It's gets really confusing when you have to make a possesive form of a super plural. There doesn't seem to be concensus on how to write it, you see all sorts of stuff. I usually go with y'all's or y'alls' and it's pronounced like y'all-zez.