Found a solution to this and will post the other related details here that will hopefully help others.
1. I confirmed that the position sensor (that detects the magnets in the globe gear) was snapped into place correctly into the holder in the base. It was.
2. Interestingly enough, if I removed the position sensor and let it hang down so it couldn't detect the magnets, the globe STILL didn't rotate fully but stopped early and returned to the starting position.
3. If I manually used an external magnet on the dangling position sensor, I could get the globe to stop, then reverse, then stop again when the magnet was present (indicating that the position sensor was functioning normally.
4. Confirmed that the magnets were in the correct location on the globe using a paper clip (from tech support):
"There is a seam all around the globe just above the rivets. Go to the side of the globe where the waste ports are and start at this seam and count UP on the track and see between which 2 holes the paper clip clings. It should be between the 10th and 11th hole. NOW, start at the seam again, only this time count DOWN on the track. The paper clip should cling between the 9th and 10th hole."
5. Now here's the kicker for me, since we bought this as a used unit on Craigslist, the power supply we were given was a 9V power supply that was enough to power the unit and rotate the globe, just not very fast. Apparently we need to have a 12VDC and either a 450mA or a 500mA adapter? So I'm guessing the actual problem was that the globe was spinning too slowly at 9V, then reached a timeout on the controller and returned to the starting position with the magnet. Using a Linksys power supply I had in the house I was able to get the unit working again with the 12V power supply.
I have to give the Litter Robot support people a lot of credit for sticking with me on this troubleshooting/repair issue (that wasn't caused by anything that they did, since I was given the incorrect power supply by the original owner). They were difficult to get in touch with, but working with them back and forth via email worked out very well for me and got me to a good solution.