First of all, Kohler doesn't make oil, synthetic or fossil, so buying Kohler oil is just adding a mark-up on the price.. 300 hours isn't a long time, I think I'd be OK with that because syn. oil does not break down. Years ago a test was performed with Mobil 1 vs standard Mobil oil using NYC taxis. I don't remember how many miles they got on the regular oil before lubricity failed due to molecular breakdown, but the test was stopped after 1 million hours and there was no change to any of the measured parameters of the Mobil 1. I've stuck with synthetics ever since. Remember, every time you use a wrench on any machine you introduce a failure mode that didn't exist before, such as a filter with stress cracks. For that reason I rarely perform any maintenance early.
You seem to have a picked up a few misconceptions about exactly what synthetic or semi synthetic oil really are .
Oil is a complex blend of hydrocarbons.
Some are gas some are liquids & some are solids .
The normal refining process just removes bits till you end up with what you can use , which might include a pile of bits you don't really want but make little difference to the operation of the fuel / oil / wax / gas / tar that you are trying to make
Synthetic processing does the same thing the opposite way by braking the crude down into all of its parts then blend only the bits you want to be there back together.
Now if you used the synthetic or a pure synthetic then some of its properties are substantially enhanced over a standard refined oil.
However that does not happen because synthetics, just like normal refined oils does not have all of the desired properties so a package of addatives has to be added or it would go off a lot faster than standard oils because it is in a substantially higher energy state.
Just the same way as iron, or copper corrode because they are in a higher energy state than their oxides .
The big difference is standard oil is at a purity level of around 98% , semi synthetics are 99% & fully synthetics are 99.9% pure .
Just like gold, 98% is expensive, 99 % is more expensive & 99,9% is even more expensive & if your pockets are deep enough or your research budget is big enough you can get 99.99% and 99.999% .
Any way synthetic still break down & oxadise just like standard oils do and every other refined material, it is the first law of thermodynamics & to date is yet to be proven wrong .
Fully synthetics are a slightly different case as they are made by reacting one of the gasses , that has been removed from crude oil during refining and then reacting with ammonia to make an oil , some are made from natural gas that has been refined but the process is the same.
Fully synthetics start life a bit cleaner than semi synthetics but again are useless for use in an engine without the addative package.
And this package will be consumed during use rendering the oil useless just the same as it happens with standard oils , but because the oil has less impurities in it , the oxidization &/or decomposition takes longer.
Now synthetics cost 3 to 4 times more than standard oils to make so a lot of total tosh has been published by oil companies to make people believe that they are worth the extra money.
In 90% of the uses there is no advantage whatsoever , and mowers are the perfect example of this so using synthetics in a mower is throwing money away.
Then again people will happily buy lottery tickets .
In a hydro drive their superiour properties & in particular superiour cleanliness is a big advantage .
Because of the brain washing that the oil companies have done , and don't forget the "fakes" who join forums like this to sing the praises of synthetics , and on face book & you tube and anywhere else where the brain dead easily brainwashed congregate , engine makers have to specify synthetic oils to "prove" that their engine is better than every one elses .
IF you are building a high precision high performance engine that is trying to extract 10 tenths of the available energy in the fuel then yes the extra money is worth it.
If you are running an engine with a lot of easily damages sensors like top end direct injection engines then the cost is justified to protect the engine sensors.
In a basic mower engine that is making 5Hp / litre they are a joke .
And if you are wondering why any one bothered to make synthetic oil in the first place, it was a by-product of the research for converting gas into petrol which was designed to reduce the USA's dependence on middle eastern oil .
Because the oil is cleaner then the exhaust is "cleaner" if you use synthetics so the EPA can enforce tighter emission controls which is one reason why zinc levels in oils are being lowered .