I have an update on my FaceTime crackly audio issue. After trying a number of things, what resolved the issue was to backup my computer to Time Machine, erase the hard drive, reinstall macOS from scratch, and then restore my computer from the Time Machine backup. Restoring from Time Machine took the most time, about 8 hours for close to 2 TB of data, even when using a hardwired ethernet cable instead of wifi.
I'm not sure why this would resolve the issue, as I think restoring from a Time Machine backup would restore all the settings for apps. But I'm glad it did, because it's now a lot easier for my kids to talk to their grandparents.
I also gained back about 8 GB of storage, so that was a nice bonus.
One thing I've learned recently is that Apple Support is really pretty good. I was able to get on the phone or chat with Apple Support in a couple minutes, max. And although they are clearly following a script (reboot the computer, set up another user account, boot into Safe Mode, etc.), they do seem to take ownership of the issue. I've actually had to contact Apple Support a few times over the past month after not using it for quite a long time, and I've been very happy with the outcomes.