I received the CM15A replacement. Followed the Owner's Manual Hardware Setup section carefully. Only skipped steps 2, 3, & 4 because I already had the AHP app installed.
The new CM15A works perfectly! The simulated switch in AHP turns my desk lamp on and off, schedules for all lights in the house and yard work, and the 3-button wall mounted switches work.
A remaining question in my mind is whether the returned CM15A was (a) bad from the factory, or was (b) it was OK but had not been set it up correctly. My guess is (a).
However, there is one difference in the way I had carried out the setup instructions: As per the Owner's Manual, I installed the batteries after connecting to the computer & plugging it into the mains. I did not do it that way while setting up previous one (the "bad" one) a few weeks ago.
Other than that I'm ready to draw a line under it, as the Brits say, and move on.
Many thanks to those who have helped me along the way.