Well, I finally solved the problem and what a saga it was! I tested everything to rule things out and it all came back to the Airport Express (not the DAC, audio files, MacBook, cables, etc). What really tipped me off to the issue was that I got the identical crackling noise out of the analog output on the Airport as I did from the optical port. Long story short, the upgrade to firmware v7.8 is the source of the problem, and downgrading back down to 7.6.9 is the solution. The audio sounds crystal clear now, and I feel comfortable considering the Airport Express to be a quality "vintage DAC" in its own right. I hope this info helps someone! Links:
Firmware upgrade is the issue:
https://forums.macrumors.com/threads/airport-express-firmware-update-terrible.2134953/
How to roll back the firmware:
https://www.macobserver.com/tips/quick-tip/macos-roll-back-airport-basestation-firmware/