If I hadn't seen it I wouldn't have believed it. Here's the skinny:
The motor wouldn't always bog down, and it wouldn't always reverse. Sometimes it would run perfectly. I originally discounted single phasing because I was thinking it wouldn't rotate at all, it would just sit there and grind.
Turns out there was a loose connection on one of the phases. There was a lot of vibration, the terminal would loosen up intermittently, and then the motor would go single phase. Once it single phased, it couldn't move the load forward and it would bog down. The chain-drive it was hooked to would yank it in reverse, and because there was much less force needed to drive the load in reverse, it would just start sailing away in that direction.
I just happened to be running the motor with the pecker head off and saw arcing at one of the Stakons (which was a phase being lost), and right as that happened, the motor did it's little magic trick.
Didn't know single phasing would do that. You guys were all over it! Thanks!
-John