Small Engine Troubleshooting Problems? Ask a Mechanic Now.
Welcome to JUST ANSWER small engines, let me try to help you !! After studying your question and looking at the results you have achieved, I think you could have a valve problem. Can you get the numbers off the engine? Kohler uses many setups, and I would like to be sure before telling you a lot of non sense.
Apologies for delay in response; changed the oil filter and did not refill lost oil. Problem appears to be solved as both valve covers seem much more even in temperature (checked couple times while running and when stopped) with power and smooth running generally restored.....was able to finish mowing a large enough area that before it would have likely overheated and started skipping before finishing....I would offer that the first oil filter was defective an for some reason not passing enough oil or as much as I hate to admit....the engine may have been slightly overfilled with oil and submerging the spray holes......could explaing issue of noticing the problem moreso when going up hill or under load......I did however check the oil level when changing and before cranking up and seemed ok.....I run synthetic oil in the engine and when fresh\clean it can sometimes be hard to confirm the exact oil level......will have a better idea of all this tomorrow when I run the mower some more tomorrow......
Ok, you might want want to look into whether this model needs the valves adjusted on a regular basis.