The fact that its moving slowly is not a mechanical problem (aka not grease/gears).
If you remove the gears of the servo, and just look at the output pinion of the motor as you move the potentiometer, you will see its speed varying. This is perhaps also the best way to center the servo/potentiometer. When the motor sans gears is not spinning, its definitely centered. (Because there's friction in the gears, you can have a slightly non-centered servo where the torque being supplied to the motor is not enough to overcome the gears' friction.)
would it be more accurate to saw the pot at the lowest level using a knife, then use pliers to zero it?
More accurate than what? It should be sufficiently accurate, though. Tweezers will also work well for pot adjustments.
Gorilla glue will work, but keep in mind that it expands a lot. You want to make sure that the expanded glue isn't getting in the way of anything.
(I've not modified a hobby servo in a few years, so I forget how much of a potential problem the glue expanding is...)