After some researching I was convinced it was either the run capacitor or starter. Since they are common failure points, I replaced both since the total cost was much less than calling a repair tech. While in there I took the opportunity to clean the coils of dust and debris.
The parts came lightning fast, and the install was fast and relatively simple as well. The refrigerator is operating correctly and whisper quiet again.
Thanks to the forums, fellow reviewers, and Appliance Parts Pros!