I studied the rather thick manual and discovered the Setup menu and its special features. Seems that the mount thought the time was PM, not AM - and it was also an hour off, thinking that we were in Daylight Savings Time. That's 13 hours off. Plus, for some freakish reason, it was also two days off, thinking it was the 5th, while today is the 7th. Odd, these things, for a GPS-powered instrument. (I also input some info such as my name and address.)
Once again proving the value of reading the manual cover-to-cover.
We'll see how it works during my next astrophoto session!