I agree. I just put a new carb on a leaf blower that never ran right from when it was new. It ran better on half choke. With the new one, it runs better and with choke off. Turns out the problem that lead me to buy the new carb wasn't the car though. It was carbon on the piston ring, causing it to jamb up, instead of springing out to seal. With that fixed and the new carb it's better than new.

I think you can buy adjusting tools for most carbs, just can't do it the old easy way. And I'll bet that running it on half choke is what contributed to the carbon build-up.

I would disagree with that last part. If it ran better on half choke it means there was some clogging in the carb and the choking is what was necessary to deliver the proper mix. Your part choke was not making it too rich where that might cause carbon build-up; it was delivering exactly the right mix.

Have you looked at the online websites that sell parts? They have diagrams that show how it's put together and you can probably figure out how the governor works and how to check or inspect it.

I know enough to know that on the typical Tecumseh the governor is actually a little flyweight thing deep in the engine and that's what moves the shaft that has the lever that is just behind the air cleaner, which links to the carb. It is not something you can get to (that I am aware of) except if totally dismantling the engine. Which may be the final fate of this engine.. The final bit of entertainment!