Ok, well the problem seems to have spontaneously resolved itself, though it could be the order in which I did things that made the difference. The audio cues are now playing like they should.
Reinstalling iCUE wasn't necessary, but I did flash the firmware, then adjusted the mic volume settings in iCUE (not sure if that affected anything) and then, rebooted (leaving the computer off for a good 7-8 hours).
As for the light, I think I was confused what was meant by 'Mic Mute Interval.' That was the setting I was looking for that controls the light blink. Just worded really strangely. So I had it set to off, rather than something like 5-10 seconds like it used to be. Now it works fine.
Not sure if this was just a glitch or not anymore, but hopefully this will help out others with the same confusion?
I will be taking closer care of the mic boom if it's really a common point of failure. Thanks for the assist though Waukeen!