Good God! We actually may be onto something here.
I have spent I don't how long trying to search " How many degrees does the moon move in the sky in one day?" You would not believe the convuluted mess you have to go through to get this simple answer. I finally found this post by a Dr. Mike Fanelli which appears to be the simplest answer you're going to get on the internet.
http://74.125.95.132/search?q=cache:...lnk&cd=3&gl=us
He says the moon should appear
13 degrees east of it's position on the previous day at the same time. This still doesn't explain the discrepancy of me seeing it at atleast 45 degrees in one day or the TC's seeing it at 145 degrees in 2 days?