Thermostatic mixing is quite common and necessary by code in some places I believe, especially if you have a gas powered hot water tank. Basically, it’s safer to heat water well above 120F to kill bacteria (things like Legionella) but then the water is dangerously hot to use, especially with small kids around.
You could test whether you have the automatic mixing going on, which blends the tank hot water with cold water to bring the temperature down, and that’s what is fed to your hot faucets.
Cautiously (when no kids or unaware adults are around using water) make a note of what the tank thermostat is set to and then turn it up to near maximum … the gas should turn on immediately and heat the water to that setting. This is not the thermostatic mixing temperature, which is normally set (fixed) to 120F or thereabouts. Wait until the tank switches off and then go around to all of your hot water faucets and test (cautiously) whether the water temperature has increased significantly. Be careful, the water could be scolding hot. If so, you probably don’t have the automatic mixing anywhere so you should turn the tank thermostat down again to where it was at a safe temperature.
This is essentially like your pre-peak super cooling with the AC. The higher the tank temperature the less likely it will turn on during the peak period. That said, if it does turn on because a lot of hot water gets used it may run a little longer.
I’m suggesting all this more to explain how the system may work rather than exactly what to do. If you understand technically how the water is supplied then you can make judgement calls as issues arise. This matches what you are doing with the AC.
Personally I would leave the water system alone and write off the modest energy debt and focus on optimizing your AC scheme. I’m guessing you have something like 1 minute of AC “on” equals 30 minutes of hot water blower “on” in terms of power use. That’s something you can quantify in Sense of course.