> I have a client coming into my hotel who demands 120 open mics ... Money is no concern. <
It's a good thing cost is no object because this will be expensive!
> How to gate? EQ? Group? Mix? <
Using gates is the simplest choice. Then the only "instructions" you have to give people is to lean in and speak up.
A good friend of mine designs systems to solve problems much like you're describing. The goal is for many people in multiple locations to all teleconference, using many open microphones (overhead), where serious DSP-based feedback suppression and echo cancelling are part of the system. If money truly is no concern, email me through my company's web site and I'll be glad to put you in touch with my friend. (He doesn't sell these systems himself, but rather designs them and codes the DSP for the company that does sell them.)
--Ethan