OK. I think it is more of a detergent or non-detergent issue. I thought maybe those classes were different in that aspect. For some reason I thought non-detergent oils were recommended in engines without a filter. Again, I doubt it's an issue in this Kohler engine. Probably the least of my worries.
Non detergent oils were designed for use on engines that ran dry sumps with external oil tanks so the crud could settle out to the bottom lower than the pick up tube thus go out of circulation which was the norm way back pre WW I
Detergent oils are designed to hold the crud in solution so that the filter can extract it easily so it goes out of circulation which became very wide spread from the late 60's on cars and the 90's on mower engines that had an oil pump
Everything else you have seen , heard or think you know is the BS used by advertising companies to convince you that brand X oil is better than brand Y oil.
In a small stationary engine running at fixed speeds with no oil pump it makes next to no difference what type of oil you use and even less if it is changed at the end of the use season.
The only important bit is the viscosity number
Your problem stems from the use of the fuel stabilizer .
When they are needed, they are good & do a good job .
However like vitamin suppliments that is about 5 % of the people who use it.
The rest of the time they mostly do no harm .
BEcause CEO's & Directors get paid bonuses , Stabil. Marvel. WD40 etc spend a fortune convincing every one that their product is needed everywhere that they are not needed .
Remove your fuel tank clean it out & allow it to dry
Replace the fuel lines & clean the carb to remove all traces of the gunk you put in there .
For the purpose of testing, start the engine and see if you can keep it running by giving it SHORT shots of carb cleaner ( better ) or engine starting fluid ( not so good ) through the carb ( the engine will knock a little with every shot , don't worry about that ) .
Now if you can keep the engine running for a minute or two like this then the problem is with the fuel supply
If not then the problem is with the ignition or valves .
If you got a backfire then the ignition timing key in the flywheel could have cracked or even sheared off and the engine is now a poofteenth out of time