Blackberry,
The following pics are from my 158-17570 machine. Although the steel ZZ cam is slightly different, it uses the same exact cams that your 158-17560 does. They also snap on exactly the same. I know this coz I had a 158-17560 too.
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You can see the little spring loaded detent ball in the side of the shaft, and the grove in the bore of the cam. This is where your problem most likely is. Considering all the old oil I see in your first pic I suspect the old oil has gummed up the detent ball and or glued the cam on the shaft.
That is why there is no need to disassemble the cam drive. Just float it in a good penetrating oil and work the cam up.
The cam has a finger grove around the sides, so you might take a pair of pliers and pad the jaws to get a better grip.
Then rock it slightly while it's floating in oil.
Joe