To me that sounds like one of the shields on the catalytic converter rattling, though you say pushing in the clutch changes the sound, which that part I don't have an answer for...
I actually had the solenoid (bendix) come loose on my '94 4.0L starter one time and the starter pinion gear would "fall" into the flywheel while accelerating or while pointed uphill. The noise was very different from that (more like a simple clicking or tapping sound as the pinion bounced off from hitting the flywheel).
It often can be hard to tell sounds not recorded with good quality microphones or audio setup (especially after it going up on Youtube), though to me that still does not sound internal to the transmission (more like a piece of sheet metal rattling rather than a bearing).