Thanks, Tuicemen.
I typically would send commands either via wall switches, the Radio Shack Mini Timer, Melloware's X10 Commander, or macros/timers in AHP/CM15. But, in order to debug, I reduced the AHP to a single room without timers/macros and unplugged the mini timer. The echoing persists. I don't have any RF remotes on which a key may be stuck. I long ago unplugged all transceivers (e.g., TM751 and PSX01) and have not reinstalled motions sensors since getting new siding on our house last year.
Unfortunately, I cannot change the house code on the four ceiling light fixtures. I really blundered when I installed them. When I redid my older son's room's floor about 20yrs ago, it was a good time to add can lights to the family room which is below his. So I opened up the floor, ran electrical, and installed the inline modules. The can light boxes are not readily accessible from the ceiling. (Rushed to do the job without forthought--big mistake.)
There is another oddity which is probably due to the echoing: for a long time there have been time slots during the day during which commands are completely ignored. (This really annoys the wife when I would tell her that you can't turn on the family lights, using the Mini Timer buttons, between 5:30pm and 7pm.) I have noted that during these times slots hundreds of the same command are repeated every second according to the Activity Monitor (AM). As an example, last night I cleared the AM and just checked it. During the course of the night "F1 ON" sent was echoed 6000+ times. Interestingly, the light never turned on--or at least no F1 OFF command in the AM. No reception of the ON command in the AM.
Our neighbors do not use X10 or any other automation so a need for a blocking filter is not "necessary." (I couldn't install the PZZ01 20yrs ago because the 4/0 Aluminum wire will not fit the opening.)
Since the AHP/CM15 is really not doing anything now (other than allowing me to use X10 Commander on my phone), I am going to unplug it and see if the "time slot" issue is eliminated.