Imagine that, an issue with the CTIS. I have attached a link to a video of my truck. The rear axle quick release valve does this, then stops, repeatedly and eventually all tires will deflate. No flashing codes. I looked at the TM, but it isn't very helpful. Also, the link to the Dana Diagnostic Tool download apparently is no longer available. Link is to video of noise.
CTIS Noise
One of my rear quick release valves did something similar last winter when I had the system connected to shop air to try to find leaks. But only when it had the tires leveled off at the same pressure as the input from the shop air. Basically when the inlet and outlet were the same, it was constantly dithering between having the QR valve shut and having it slightly open. So it would sit and hum a little, although mine was quieter than that and I doubt I would have heard it over the truck running if I hadn't been running it off the air compressor.
I don't really know where that leads for troubleshooting though. I would have thought as a whole assembled system that the input pressure should always be higher than the tire pressure, so it should never get to this point. Is it possible you have a restriction upstream, either in the CTIS inlet air filter or the solenoid box, where it gets enough pressure for the initial 120 psi check but then is flow restricted enough that the pressure on both sides of the QRV are essentially equal when filling tires?
I have not had it happen myself but I have seen folks say that a leaking hub seal makes a squealing sound, too. Are you 100% sure it is the QRV? If in any doubt, take the output line out of the solenoid box and hook it to a regulated 70 psi shop air line to pressurize the whole CTIS system and see what it does without the added sound of the engine running.