I think I may have stumbled across the solution to my own problem. When you mentioned the half-height button, I went looking for it. Problem is, I had purchased one of those silicon "sleeves" (or whatever you call it) to kinda protect the phone if it should be dropped, and make it easier to hold on to.
Problem is, the sleeve doesn't really have cutouts for the buttons on the side, and you are supposed to push those buttons right through the sleeve. But when I tried to push that half-height button through the sleeve, since the camera button was slightly taller, I would end up pressing that button instead, and the camera would come on.
I experimented with taking off the sleeve and not only could I press the half-height "off" button, but now the phone goes to sleep after however many seconds just as it is supposed to.
So, bottom line, the silicon sleeve was doing something, I'm not sure what (pressing one of the buttons continuously, maybe?) and that kept the phone from going to sleep.
The sleeve was just an interim solution until I find a case I like. Meanwhile I think I am going to take a razor blade and cut openings in the sleeve for all the buttons to see if that frees them up so that the phone will go to sleep as it should.
So, in a roundabout way, your suggestion about the half-height button solved my problem.

Thanks so much.