Yes Trevor, if you post pictures of the back of the governor rack and pinion assembly that would be useful. As you said, we hope someone else will be able to post a picture of the back of one in working order, and we'll see what is needed to get yours right.
I think we will need pictures of the other end of the choke link, where it attaches to the carburetor. The key question is whether there is a "lost motion" mechanism there, or we have to make the link move exactly the right distance to get the choke fully closed and fully open. I would hope to find a spring-loaded stop at one end of the link. Incidentally, this is what P/N 261610, Link - Choke, is supposed to look like, before "tenant's improvements" are taken into account:
As you know, reconnecting all the safety switches is essential before the mower will be back in working order. If you can't have a coupled choke you will at least need a dashboard choke control, but putting things back the way they came from the factory is the best solution, because it has been tested and developed to get the bugs out of it. (Also, you can probably get parts for it if it is to the original design.)