I ordered the entire water and ice dispenser and refrigerator control unit from AppliancePartsPros.com and then watched the video for the removal of the old one and installation of the new one, at least three times so that I had the sequence memorized and felt comfortable with the process. Thanks for providing that, by the way.
Then I opened the breaker for the refrigerator and used TWO putty knives, not one ... 'cause sometimes you need the extra one to hold in place the work you had already done loosening the unit. Once the unit was out, I removed the wiring harness, noting that all of the plugs were unique (so I could not screw up putting it back together). Then I cleaned the inside of the refrigerator compartment with white vinegar (we had potassium salts build up from our water softener).
After that, I hooked up the new unit and literally popped it in. Closed the breaker and reset the parameters to those we had set with the old unit.
This was a very easy replacement. And I am so glad we found AppliancePartsPros.com.