Hi Chris,
Unfortunately, I was unable to determine a solution to this problem. I spent some time on the phone with a technician who ran me through the steps in my first post above. When the paper jammed again, he said that I'll have to buy a new printer. :^) How convenient! They did give me a good discount on a new one and I just ended up buying the MFC-L2750WD, which has been working really well since then. (Fingers crossed.)
I'm with you, though, in that there is some sort of sensor that is stopping the paper from feeding right through. It could be something as simple as a loose belt which is not allowing one of the rollers to spin at its proper speed which is being picked up by a sensor of some sort, most likely optical.
Good luck to you.
Cheers,
Barry