Gene, you're not going to believe it, but I ordered the part -- then plugged the refrigerator back in (because I had the idea that maybe the line to the icemaker was frozen, so I'd been letting it thaw for several hours). A half hour later, I hear ice dropping into the tray. Murphy's Law.
I'm not sure if thawing solved it, but the light is no longer blinking and I've got ice. I put the ordered part on "hold" and I'll see if the icemaker continues without issue.
Thought you might like to know about it. Blinking green light isn't necessarily fatal (knocks on wooden desk). I'll be sure to let you know if this changes.
Thanks again for the help.