Okay, this is finally resolved! Because of various work and life issues, I had to set this problem microwave aside for three weeks. In the meantime, I was lucky to locate a similar microwave (this one with the convection oven option) on Craig's List, and I took a chance, since because of the somewhat unusual size configuration, another model would have required some cabinetry and back splash changes in order to meet the Wife Acceptance Factor. The substitute microwave was priced very low and works and looks fine, so it took some pressure off of fixing this one.
Anyway, I finally had a chance to get back to looking at this one. As Rick mentioned, it was driving me crazy not knowing what was wrong. It's always good to step away and come back with a fresh mind, and a couple of weeks apparently freshened my mind.
I started going through all of the steps I've taken from the original replacement of the keypad and related User Interface Board to fix the "ghost" beeping and program changes, and I realized that the intermittent reset problems happened after the replacement of those boards. And of course, the replacement of the boards required removing the door and reinstalling it, in my case, multiple times. So, I inspected the wiring carefully and saw some slightly crushed areas where the wiring might have become caught in the hinge when reinstalling the door. Testing showed that one wire was in fact very intermittently losing continuity. So, I spliced that crushed area, soldered the wire and covered it with shrink wrap. Everything worked properly after testing, and it continues to work after I put everything back together.
So, I've learned my lesson ----- Check the relatively simple things first, and be sure to think back through all of the steps you've taken previously. If I had done that earlier, I could have saved myself a lot of grief, and I wouldn't have an extra microwave.
Thanks to Rick for all of the valuable suggestions! This website was very helpful in all of my struggles.