I remember that rig but never owned one and don't recall the drive mechanism used.
Sounds like a "planetary drive" mechanism, and 2-speed versions as you describe were pretty common. Does the drive mechanism mount to a panel or chassis with two bolts or screws and can it be decoupled from the VFO shaft by removing a coupling?
If so, I'd remove it entirely from the rig and then do what KE3WD suggests. I've "repaired" these several times (if that's what you actually have) by using solvent in an ultrasonic cleaner (like what jewelers use to clean jewelry, we happen to have one at home which I mostly use to de-grease electronic parts) until it's absolutely clean, then just lube the bearings with an injector that looks a lot like a hypodermic needle. Works every time.
What if soy milk is just regular milk introducing itself in Spanish?