Here's the video. My beloved mom helpfully comments about how obviously terrible the noise is, lol.
Thinking the problem through a little more, due specifically to the fact that the belt is a serpentine instead of one that only drives the S/C, I can now imagine that the noise is the belt slipping (most likely on a pulley other than the S/C). I am not certain everything that this belt drives, but either the oil pump or the power steering pump might have an early resistance that builds up and fades after they get up to speed. This might also explain why it only happens when cold. Questions:
1) What other accessories does the belt that drives the S/C also drive?
2) I have a feeling that my shop tensioned the belt as much as could be done without the right pulley, but how can I check and possibly tighten it further to see if it helps the problem?