Hi Mick, here is the Illustrated Parts List for your engine:
http://bsintek.basco.com/BriggsDocumentDisplay/Z6lttJVJ1DajI.pdf
Here is the Operator's Manual:
http://bsintek.basco.com/BriggsDocumentDisplay/msoBGL-K_ny7tH217FzoPu.pdf

You didn't post the Code, so we don't know when it was manufactured. However if you look at Page 7 of 17 in the IPL, you can see what the parts of your governor mechanism are supposed to look like. In the Operator's Manual it is clearly a rack and pinion unit (page 7 of 14).

I think the solution to your problem is to get the correct rack and pinion parts from a wrecked engine. What you are attempting would require a long development job to get an inferior result. In my opinion it does not make sense to make a silk purse into a sow's ear.