I can't help you get your aircon into Home Assistant (hopefully you've got that covered).
But as to your automation plan, check out this HACS integration:
Versatile Thermostat. It does exactly what you want - you set the "underlying" device (which will be your aircon), and you can set an external thermostat (you can create an "average" thermostat based on your 3/4 thermostats just like you planned).
The integration will then control your thermostat and adjust temperatures up and down to keep the external thermostat at the temperature you require. It does it all in the background so the dashboard looks like a normal aircon dashboard, but underneath it's doing all those calculations and adjustments for you. It also has adjustments for how fast you want it to adjust to temperature changes and whether to take outside temperature into account.
I use it quite successfully (although my thermostat is very close to the floor so the temperature fluctuations are quite wild because cold air drops much faster than you think).