The current setup uses a pro-grade Yamaha MG166CX mixer with dual / master outputs, aux, inserts, effects, compression, blah blah blah...

It's TOO COMPLICATED for general day to day use. 99% of the features are never used, and most people don't know or care how to use many of the features like compression or the effects system.
Most people want basically to flip a switch or push a single button, and done. They don't want to have to deal with "hmmm what did the last person do here on this audio-nerd mixer, and what all do I need to undo or zero out or rebalance or disconnect / reconnect, just so we can do announcing for tonight's basketball game?"
But I also don't want to dumb the system down so much that someone who wants to use the fancy external mixer can't do it because all the facility inputs and outputs are locked down to the architectural mixer. Or worse yet some outside "audio expert" tears out the "simplified" mixer wiring to get direct access to the microphone channels and amplifier outputs.
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At this point what I am thinking is that apparently each XLR input should be split to go to two separate architectural mixers, one for the gym, and one for the stage. And there should be a third output that is a bypass that skips all that and comes out to an XLR socket for a pro to use.
Meanwhile the two architectural mixers should have exposed XLR inputs for a pro to plug a external mixer into them, if that's needed to go to the gym and stage speakers.
Probably something wired like this on the back:

And this simple user interface on the front:

Though, I am looking around the Peavey website and I don't see an XLR distribution amplifier, so I don't know if this is workable using all Peavey architectural audio components.
The AutoMix Control 8 seems like overkill since I don't need any of the external control features, just the 8 knobs + master knob.
The MMA 8752 also has 8 inputs, but I don't need the amp functions. I already have a rackmount Ferret D and a 2-channel amp, so I just need balanced out to the ferret (used in "hands-free, no interaction required" panic mode only).
Obviously, an all-digital system would be nice, but I don't want to be spending thousands of dollars beyond the analog mixer / XLR distribution amp component costs, to implement a gilded touchscreen interface. (I can't find any direct list pricing for the nTouch 180 touch screen so it's most likely going to be very expensive to custom-implement, vs analog controls.)