I don't know that the rocking is an issue persay. If you look closely at the wheels. They tend to move in an orbital motion/ back and forth based on the drive rod position because of the excessive play that Lionel has had in the axle bushings for the last several years. TMCC and early Legacy locos have much tighter tolerances and minimal play.
This motion isn't noticeable when the loco is pulling a load on track.
If you turn the loco upside down and grab a pair of drivers between two fingers and twist you will feel this play.
I won't challenge Alex's advice, he's certainly more knowledgeable than me, but that forward chatter sure sounds like gear noise.
Lateral play in both the axle shaft and the motor worm allow the gears to move to one end of the contact surface or the other depending on the direction. In your case, possibly the forward direction has the mating surfaces of the gears going too far to one edge.
I'm curious if these hudsons have the intermediate gear on a shaft in the gearbox above the center driver. I've found this intermediate gear and shaft to be a weak link in the newer Lionel gearboxes. while this gearbox is key to ultra slow speed performance. It adds 2 more gears to the gearbox, and is less reliable than the typical worm and axle gear setup.
I've had one of these intermediate gears be faulty out of the box, and a few years after warranty repair the shaft bushing showed significant wear so I parted with the loco.
This intermediate shaft can usually be seen behind the "motor driven" driver between the spokes, although it may be hard to see through boxpok wheels.
This intermediate gear shaft can be seen in this legacy mohawk video ( not mine) starting at the :22 mark just behind the 3rd set of drivers. : https://youtu.be/0y60BIICyng