centxn, thanks for the additional details, which clear up most of my questions - the choke mechanism, which Honda calls an automatic choke, is now fairly clear.

So far as the actuation of the throttle butterfly is concerned, I am doubtful that this can be done effectively through the small spring (very similar to the anti-oscillation spring on the older design) which is currently the only connection to the butterfly. However the first step toward clearing this up would be to adjust the governor, so that it is eliminated as a possible source of the problem. If the problem still remains after adjusting the governor, we can discuss it further.

Here is the section from the free-on-line manual, describing how to adjust the governor linkage:
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Please read the next part while referring to this picture:
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It is fairly uncomplicated. Essentially you loosen the clamp bolt (yellow circle) at the bottom of the governor arm, pull the top of the arm (green circle) all the way to the right, and rotate the governor arm shaft (red circle) (on which the bottom of the arm is pivoted) clockwise as far as it will go, by using a small wrench on the flat shown in the red circle. Then, holding both arm and shaft in this position, you re-tighten the clamp bolt. The purpose is to remove any slack so that the paddle on the far end of the governor arm shaft, inside the crankcase, is in contact with the plunger on the centrifugal governor mechanism.

The difficulty you had in making this adjustment was probably caused by minor corrosion of the joint between the governor arm shaft and the governor arm. After backing off the clamp nut a couple of turns, just hold the arm stationary, and rotate the shaft with the small wrench, to free up the joint.