Your setup should look similar to the pic below. You should be able to move the link coming from the bi-metal thermostat without to much difficulty. It should move that black arm forward which opens the choke. If it doesn't, I can guess its one of three things.
The arm I mentioned previously is...
I was always told that if you can't catch your fingernail on a grove you can avoid a hone, but others here know vastly more so I'd wait to hear what they say.
So there is a link that runs from the thermostat on the muffler to a little plastic arm that pushes the choke open and closed when the muffler gets hot or cold. If that is in the wrong position in relation to the plastic arm with the spring on it, it can jam the choke movement.
So I got my strongest readers out and there is no tip on this K20-WYL needle. I'm not sure if I got a factory dud or what. I got my wife's camera that has a better lens and took a snap of a needle from a k20-WAT on the left and the K20-WYL on the right. Both were wiped with brake clean to remove...