I just wanted to report that after an update (I'm not sure which one), this is resolved. The little status light on the side of the computer now fades on and off as the computer is sleeping, as it should. I also noticed it's started to beep (or play a little sound) when I open the screen of the laptop, presumably to indicate that it's now waking up. So, as I've seen with other little issues, if you are patient, the Linux community eventually fixes it. Take that, Windows!
Thanks!
--neal