FRANK - There's a writer for Red Power Magazine that writes a column called "The Tractor Doctor" that in the new Nov/Dec, '2010 issue addressed the Kohler sticking exh. valve problem. He says it's due to carbon deposits on the exh. valve stem due to the use of NON-LOW ash motor oil. It tightens up the already tight tolerance between the valve guide and valve stem.
My K241 in my 72 used to stick the exh. valve slightly on long hard pulls but would never stall, just start sounding "Hollow", slow down, and I'd hit the clutch or turn off the mower and it would cool enough & free up the exh, valve and run O-K for a while longer. When I took the engine apart it had a thin layer of very hard carbon on the exh valve stem just like the picture in this article showed . It also had a layer a quarter inch thick of dirt & crud stuck to the front & sides of the box that the valve springs are in which I'm sure kept it much hotter. The problem got much less frequent when I richened up the main fuel needle a quarter turn or so.
So I'd turn the top screw on your carb counter-clockwise a quarter turn and see if it gets better, if so, turn it another quarter turn, if it still bothers I'd pull the head & breather cover and replace or clean the exh. valve. And yes, you can replace just the exh. valve, I ALWAYS replace the exh. valve on an engine rebuild, but have never replaced an intake valve.
My K241 made a very distinctive sound when the valve would stick, I had the little "Pepper-shaker Muffler" on it, your BIG chambered muffler may quiet the exh. enough you can't hear the change in tone.
I tried MMO in that K241 for a couple tanks of gas and it made NO difference, all the plug does is light the fire in the combustion chamber. But turning up the main fuel needle made an instant change, it cools the combustion flame temp. which lowers exh valve temp.
Also use the Stellite exh. valve, more expensive but well worth the added cost on a hard working engine. Far as rebuilding the rest of the engine, piston, rings, etc, without knowing more about the engine it's impossible for me to say. I'd fix the valve first, change to Low Ash oil and run it.