I recommend trying the PingPlotter with pings to 8.8.8.8 if you don't know the IP/hostname of the CC server (would have to either get from the company or by using a packet sniffer like wireshark or built into a firewall) as well as one to the head of the network. You need to see whether there's any difference between them. Do this with a laptop plugged into a jack where you can plug in a CC machine. If there isn't, and you're not dropping to 8.8.8.8, plug the machine into the same jack and test the CC a bunch of times. If the laptop seems great the entire time and the CC machine has random issues, it might be a coincidence that the change happened after you made changes and it's really the CC company's end. You could also try connecting the CC machines to a separate network somewhere else if possible (it sounds like this would be difficult, though).
+1 for bridging the starlink and using your own router/firewall at the head of the network. 1500 MTU is standard for nearly any regular network device so you shouldn't have to worry about MTU issues if starlink is already using standard 1500 MTU.