Brian E - I think you're jumping the gun a bit. I wouldn't be calling it an "overhaul". I know it's a loosely used term but would normally imply you've been inside the engine. I have to say you're working towards a major tune-up, and will be once you decarbon the head and piston, and check your valve adjustments (accessed by removing the breather cover).
Here's my take based on your additional information. You probably have a little problem with everything.
You said the points were gapped at .30 and you wnt to .25. You might have been thinking of the spark plug, but even then you left a .0 out of your numbers. The plugs often come gapped at .030 and you'll find alot of Kohler spec charts showing .030 for the K-series engines, but I'm pretty certain Kohler and IH spec'd it at .025 for our Garden Tractor application. I've always found .025 to run the best myself.
The points are supposed to be .020, or thickness of a matchbook cover if you still happen to have one. But as I mentioned before, that's only the starting point to get the engine running. You have to re-gap the points to adjust the timing and wouldn't surprise me if you end up at .022 to .023. Go ahead and barrow the timing light and study up the manual, and then find the site hole in the flywheel shroud and start looking for the S or SP mark on the flywheel. I'm gonna bet your marks are rusted over and you're gonna have to rotate your crank very very slow until you can see them, and then mark them with some chaulk, white paint on a Q-tip, or something to make them show up well. There will also be a T (Top Dead Center) mark and it will be close to the S or SP. Sometimes you'll see the T first so I just wanted you to know you're getting close. When you do set the timing make sure you're dead nuts on the S or SP. It's gonna take you a little time and effort but once you get it there along with everything else you've done for your major tune-up you'll be surprised how quick the engine starts - I used to say when it all set correct it starts "almost before you turn the key".
We haven't talked about checking and adjusting the valves but it's pretty easily done. You haven't had any symptoms of a valve issue but I think Kohler says they should be checked and adjusted probably at the same interval as the decarboning. You do have to dismount the carb to get the breather cover (also called the valve cover) off and have sufficient access. Some guys might do it without removing the carb but it's hard to work around it. Again, study the valve adjustment info in the Service manual.
Once you've done the de-carboning and checked/adjusted the valves you'll have your major tune-up all done. This is the point where you can really decide if you need a new muffler. If you're still getting the backfire at this point then it's a good chance you have the carbon in the muffler and need a new one. You can still let the engine idle for while before shutting it off and it probably won't backfire, but I'll bet one of the times it does backfire it's gonna blow the cap end off the muffler (even tho you didn't post any pics yet I'm pretty certain I know exactly what your muffler looks like if its the correct original bullet style. The cap is probably all rusted up and may even be a little loose just waiting to blow off and a backfire will do it).
On your PTO engagement, because your unit sat so long I'll bet the belts are pretty well dried out and stiff. Most likely the first engagement was the belt slipping on the PTO clutch until it got a little hot and started grabbing. It's probably working better now and maybe ok but you need to make sure the tension is set correct on the PTO to deck belt. I'm pretty certain the setting instructions will be in the deck manual.
As for the tensioner pulley on the deck itself, it's not adjustable. It's mounted on a spring and sounds like your spring may be getting a little weak, or it could be the belt is also stretched and hard, and slipping, causing the tensioner to bounce. Best to just keep trying it and run it a little longer. But all this after you grease it all up. Hopefully your bolt holding the tensioner spring is the style with the grease zerk on top so you can get some grease down into it. I really wouldn't recommend removing the mounting bolt since most of the time it snaps off and then you need a new one.
I will add that you mentioned going up hills without hesitation. That's good!!! Sounds like your engine could still be pretty strong.
Another thing I do "not" see in your list of things done is an oil change. Supposed to be every 25 hours of operation. If you haven't done it yet you need 3 pts (1 and 1/2 gts) of SAE 30W. You can study up info on the best oils. You can spring for some "low ash" 30W from one of the sponsors or a local Kohler authorized dealer but I don't think it's necessary at the point you're at. You might read some earlier posts where Mobil Synthetic 5W30 is being recommended, but I wouldn't go there yet until you know your engine is running good. I'd just get some good straight 30W oil and change it so it's nice and fresh, and then check it often to see if you're burning any. Wouldn't surprise me if you burn down to the low mark after about an hour of running time, but I think you need 4 or 5 hours run time on the engine after it's all tuned up good before you decide if you have an oil burn problem.
And finally, you didn't mention a new air filter. Best to get a new one and then recheck all your carb adjustments.
Hope this helps keep you going.
