I was able to easily diagnose the likely causes by searching this website, which was a big help. I narrowed it down to either the Run Capacitor and/or the Start Device. Not wanting to do this twice (or pay twice for shipping) I ordered both and installed them at the same time. Still don't know which part failed, but my Whirlpool GB9FHDXWS04 refrigerator is working correctly now.
The companion how-to videos for each part were especially helpful and relieved any apprehension I had about attempting to repair a major appliance.
Honestly, I found compatible — but not OEM — replacement parts on Amazon for cheaper sourced from all over China, but I decided to buy them from Appliance Parts Pros because A) I instinctively trust the part quality, and B) I just appreciate this business model. I'm sure I'll bring my business back when the need arises.