An update: I spent a few hours scraping and washing (with spray brake cleaner) the impacted black goo out from between the cylinder fins and from behind the valve adjustment chamber. I got most but not all of it, as I did it with the motor in place. Used up a full can of spray brake cleaner, and a full roll of paper towels. I had a long thin spatula that I used to reach in and pry out the goo. I also replaced the coil, and checked the valve clearance (exhaust was only 0.006 - too tight!). Also installed my fully adjustable Kohler carb.
So.... Starts and runs much better now, and does not cut out like it did before. Air flow out the front of the tractor seems much more forceful as well. Maybe engine had been running too hot because of blocked fins? I also did the water-spray trick to (hopefully) purge carbon from the combustion chamber.
I am wondering about the source of all the oil that gooed everything up. Looks like it was coming from the flywheel side of the motor, though hard to be absolutely sure. I suppose that might mean a bad seal..... Or maybe some previous owner just over-filled the crankcase?
I'm not really up for a complete engine teardown, so I will keep tabs on how oily the motor gets. This is my "parade tractor," not a work tractor, so I am hoping to just baby it along. No blue smoke when running, so cylinder and valves can't be too bad.