Looking at the speedo I have on my desk, I would have thought that the cogs are for the odometer and don't impact on the speedo. Maybe you disturbed the potentiometer that calibrates the speed?
As you have found the other link I guess you know where the potentiometer is, and that you can turn it with a small screwdriver so I won't go over that again.
I ran the speedo separately from the instrument panel by connecting up power, ground and signal to the back, using a small terminal block as a plug, terminals as per photo. The "pins" to go into the speedo are short bits of paperclip. You can see one in the block in the photo below.
I have made up a power/ground feed from a spare plug that goes into the lighter socket, with a couple of wires soldered in but you can connect to anywhere you know there is power and ground.
The signal feed is a long wire connected to the wire that feeds into the plug at the back of the cluster. On my automatic car it is a grey wire going into the plug with four wires. I can't be sure it is the same for yours but you can trace it on the circuit board if you don't know.
Having hooked it up, have your lovely young assistant hold it whilst you drive at a nice steady speed as shown on your TomTom or whatever, and then get her to tweak the potentiomer until you get the speedo where you want it.
It all sounds more complicated than it is in practice,and it is so much easier than putting the speedo back into the cluster and taking it out multiple times for trial and error.