Excellent description of your problem Todd! Hopefully, it won’t be too hard to help you. Just a quick question; you need to make sure you have the incoming always on AC circuit power to the Aeon and from your diagram I can’t tell what you have on the 2wires+ground cable. The incoming AC power will connect to the 2 and 3 terminals. To verify if you have incoming power line use a volt meter across lines C and A by first tripping the breaker, remove line C from the 3-way switch Common terminal to isolate it, reapply breaker and measure for voltage. If it is “dead” that is the line that is probably going to the lights (load). If dead reconnect the C wire and then go to your other 3-way switch and do the voltage reading steps disconnecting the common terminal wire (usually a black screw) to verify you have successfully located the always on AC power. Once we verify which wire cable at the 3-way switch is your live AC power I like to label it with the breaker circuit number. Now we have to determine where your lights (load) wiring is. In your diagram I am assuming you are showing ALL connections in that gangbox, there are no other wire nuts (that could be the power passing through), yes?
If yes you could be wired like this below but in reality the incoming power could be feeding in at any light or switch gang box.
It is possible that the AC live power is going to one of your light fixtures first before going to one of the 3-way switches. Here is a diagram similar to your setup that might help you locate the power source from your breaker. The electrician typically will pull the live wire into whatever is easiest and least expensive which usually means the box nearest to your breaker panel which could be one of the light fixtures or even one of the 4-way switches. I found this diagrams that might help understand what we are looking for.
PS - The terminal blocks on the DSC27103 don’t connect real well to solid #14AWG wire that you typically find in your 15amp lighting circuits. I ended up making some stranded #14AWG pigtails and wirenut that into the solid #14AWG house wire.
We may need to use the extra wires. Are these spare wires not being used in the cable or they just loose? Are they running to each the 3-way light switches? I was curious if you knew why those got installed. The extra wires might be needed to get either the load or line wiring back to the Micro Switch. Aeotec shows two ways to connect into a 4-way system, one is with a live wire and one without so we just need to figure out what you have and what you want but more than likely it will be the w/Live version. I uploaded both the 4-Way w/Live and 4-Way No Live diagrams here for reference