Thanks for the update Mike. The inlet and exhaust valves on the GCV engines use the same cam lobe, so the only factor that could cause the actual valve movement to be different between inlet and exhaust would be if the rocker arms had different lever ratios. They are different parts of course - one is a mirror image of the other - and I don't know their lever ratios, but I doubt that they are substantially different from each other. Restricted movement of the exhaust valve is a good match for the symptoms you have observed (recurrent breakages of the exhaust rocker arm).
Because the GCV engines do not have a detachable cylinder head, the usual way of addressing this problem on conventional engines (just removing the head and dismantling it) is not available. However as you have suggested, there are work-around approaches that can at least allow you to investigate without dismantling the whole engine.
There is a trick commonly used to prevent small engines from rotating, and it can be used to hold your exhaust valve in the fully-closed position, and move it up and down slightly without damage. I do not recommend directly using the piston to support the valve while you remove its retainer, because the consequences of having it drop a bit further than you want are so severe (you would have to split the crankcase and remove crankshaft, connecting rod and piston to fully lift the valve and refit the retainer). Instead, you can remove the spark plug and slide several feet of soft cotton rope into the cylinder, ensuring that you keep the trailing end of the rope outside the cylinder so you can use it later to pull the rope back out. You might consider knotting that end of the rope so it can't go through the spark plug hole. Then you can rotate the engine so that the piston pushes the rope inside the cylinder upward until it fills the combustion chamber. (This is the reason to use soft cotton rope, not ordinary rope or cord: the cotton rope will shape itself to fill the combustion chamber without leaving voids, one of which might allow the valve to drop too far into the chamber, when you have removed the retainer and spring.) Lock the engine in that position so it will not rotate while you work on the exhaust valve retainer. Then you can remove the retainer and inspect it, the top of the valve guide, and the valve stem. You can also rotate the engine slightly if necessary, to move the valve up and down. Be very careful, though. If you allow the valve to lower itself just a little too far, and it jams in the guide, you will have to split and dismantle the engine. That is not an extremely large job, but I think it would be very annoying to have to do it just because you lowered the valve and could not get it back up.
Once you are in a position where you can move the engine a bit to check whether the valve moves freely, and whether the valve retainer and the top of the valve guide show signs of heavy contact with each other, we should be a long way further ahead with understanding the underlying problem.
