Bigbore, I have read all of the other replies and I disagree with several of them.
What these well-meaning members probably do not understand is that your engine is a Kohler K, not a CH or Command Pro. Those have pressurized lubrication and a full-flow oil filter. Their lubrication needs are different than that of the splash-lubed K engine that has the valves in the block.
Do not take my word. Go to Kohler.com and look up the K-series engines. Kohler has never changed their recommendation that straight grade 30W detergent oil be used when the ambient temperature is above freezing. Below freezing, the use of 10W30 is suggested but with a closer eye on the dipstick due to a slight increase of oil consumption due to the lighter weight oil.
While it is true that sludge and other byproducts of combustion will coat the inside of an engine that uses non-detergent oil, this is not a concern when that usage is a mere 5 hours. Once you switch to detergent based 30 weight, anything left behind by the non-detergent oil will be emulsified by the detergent oil and flushed out with the next oil change. If you wish, change the oil again at 10 hours. It cannot hurt and the cost is minimal.
If you trust your machine shop, then you should abide by their instructions because they are the people guaranteeing their work.