[Water Warrior 2]

Another idea here. Pull the tank to expose the choke cable route through the bike. Pull the entire cable through the bike towards the bars. With the cable still attached at the bar you should be able to suspend the cable above the bike and allow oil to drip down in the cable sheath and limber up any grunge in there. Wrap a rag around the choke lever assembly to soak up any drippings. Penetrating oil first and after things are loose and working well just do it over with a light oil to provide future lubrication and prevent binding or corrosion.
While you are oiling you might want to give the throttle cables a drop of oil to smoothen things out. Not sure about the clutch cable though. If it has a teflon inner sheath do not oil it. Oil does not play well with teflon. Of course if the teflon is already binding oil will make it work well enough till you get a new cable. My Vstrom has a teflon sheath in the clutch cable and it works very nicely after 6 years.
From the sounds of it, your GZ has waited a long time for some TLC and some one to take it out where it belongs. Get things working and the GZ will certainly reward you with what it can do.