Hey, just to wrap this up...
I think I've found the source of the problem! Though it did not, for some reason, show up as a Running app under Settings, I saw in an Android Info app that the app Timerific was running!
If you don't know, Timerific allows one to control Android settings based on time. I used it before I made the move to Llama, which is similar to Timerific and Smart Actions, but far more flexible than either.
Anyway, Timerific had re-installed after I did a Factory Reset, with a set of default actions. These included going to Vibrate at certain times.
I really appreciate your assistance. The fact that the only real suggestion that fit my "symptoms" was Smart Actions, or something like it, made me dig deeper and find the older app that I didn't realize was back on my phone! My Maxx >seems< to be working the way I want it to now!!