OK. Problem is now, apparently, fixed. I uninstalled Google Calendar app and set up the built-in HTC calendar app to sync with my Google calendar. Also made sure notifications were on in settings. Took a while, for some reason, but now both time and location-based reminders are coming through for the first time: alarm, LED flashing and notification bar icon (finger with bow tied on it). Clearly, the problem was conflict between Google calendar (a somewhat better app in my opinion) and the one that comes with the device.
:: Verizon HTC One--purely stock and lovin' it