I have heard the same thing and have had a problem or 2 if I try to start it hot so I just never shut it down till the job is done.I have the same engine. The engine fires right up every morning when the engine is cold but if I try to start it when the engine is hot it floods every time and takes several minutes to start up. The engine has been this way since it was brand new. I’ve heard it’s a common problem among 40 horsepower Kohlers. Do you have the same issue?
Even if I have to drain mid job I will idle it down, pop the waste tank lid and drain but never shut it off.
I think it has more to do with a vapor lock problem because I have actually restarted mine quicker by closing the choke for a second or two with the throttle half open.