Stew, I don't know how much you know about these little IC engines, so forgive me if I'm too elementary or go into too much detail here. But maybe those who've never seen how these work will find this of value. And, I don't profess to know about all the different designs for hit-and-miss governors, so I'll just describe the one my Upshur.
The hit-and-miss governor works by holding the exhaust valve open while the engine coasts (the "miss" mode), and then allowing the exhaust valve to close normally so that the piston can create a suction on the intake stroke and draw in fuel when the engine needs to fire to get back up to speed again (the "hit" mode). The regulation of the hitting and missing is by a system of weights, springs and levers.
Those brass pieces on the outside of the flywheel with springs between them in the picture above act as weights and are on the ends of two arms that poke through a couple of the holes in the flywheel. Centrifugal force moves the weights away from the axle when flywheel speed increases and the springs pull them back toward the axle when the speed decreases.
In the pictures below, you can see how the arms are hinged on screws on the inside of the flywheel, so that as the weights are forced away from the axle, the arms push against the inside end of a spool and move it toward the flywheel. And, as the spool moves over toward the flywheel, it in turn forces another lever to swing over and interfere with a stop block on the exhaust valve pushrod, holding the valve open until the weights are pulled back toward the axle and the arms allow the spool to return away from the flywheel. On my Upshur, a small piece of brass sheet forward of the larger gear acts as a counterspring to hold the lever away from the pushrod when it's supposed to.
The picture on the left shows how the pushrod is free to act normally prior to a "hit" while the picture on the right shows how the pushrod is held in the open position after the hit, while coasting (my fingers are holding the weights apart, not squeezing them together).
I didn't make any provision to prevent the spark plug from firing during coast. Since there is no compression or fuel intake during coast, the plug still fires, but on an empty cylinder.
Dave, one additional item to your original question. If I did it again, I would definitely allow that extra room on the cam side of the crankshaft for a larger spool, one with two sections: one section for the weight arms and the other to capture the end of the pushrod stop lever, so I could eliminate the brass sheet spring. It took me a while to get that spring balanced with the weight springs for proper coasting. I don't think I've got it optimal yet.
Hope this helps.
Rudy