Well, Amazon came through and delivered my Rachio same day. So, today I removed the old system. I started with the wiring harness...which despite being a complete rats nest, did have labeling corresponding to the manual and to the wiring diagram of the old Rainbird unit.
I used a label maker to label the outgoing wires to the solenoids, as I wanted to make sure that I could account for the wires when re-attached. Interestingly, one of the reasons my old rain sensor was not working was that it was not actually attached to the unit...though that was something that the old homeowner may have had some frustration with too!
After labeling all of the wires, I removed the old unit from the wall and mounted the new unit.
Re-attaching the new unit to the old wires was very simple.
After that I activated the unit without any issue.
Now, all I have to do is get my backflow valve inspected and turn on the water!
Programming of the zones was pretty simple too!