Yes they should move in unison. I think your problem exists in the cases. Doesn't sound like the arm off the governor is engaged or there it some damage.
If you pull the valves open and use some gorilla tape to wrap around and keep them open you can get a hint as to what the future is.
I think this one is coming down.
Meaning you are going to tear it down again. That cam on the end of the shaft would be a prime concern. I seem to recall it riding In a slot on that spring loaded shaft that goes with the governor arm. But it's been about a dozen years since I have seen one. If I was home with the manual I might be a little more help. Did you have the governor apart?
well just being a mechanical critter with what looks like everything in working order it will just be a matter of correct reassembly and then adjustment.
i know right where it is. if you want me to fax the pages anywhere i am willing or you might as well have the whole manual.