That sounds like a speedometer cable binding at/near the transmission to me. That is exactly what my dremel tool extension cable sounds like when I get it in too tight of a loop/radius. I would disconnect the speedo cable and see if it goes away. If the cable is clipped to the floorboard to keep it in place it would make a perfect sounding board for it.
Thanks (and I agreed with you initially because that's what it sounds like), but as I posted, the speedo gear and cable are no longer suspects. In fact, the speedo cable is disconnected at the transmission at the time I made the video in the hopes that would have cured it. Sadly, it didn't.
