Bill J - in response to your FWIW, I suspect your K241A is original as well. There sure seems to be alot of discussion about the "S", which is a Kohler indication of electric start. In your case the "S" is missing. I have a theory -Could it be Kohler left the "S" off for savings? (Like one of those mattress companies?). Joking aside, I've had several older narrow frame tractors and they all had the "S" as part of the Model No. And I've had several wide frame units that did "not" have the "S" on the Model No. I always wondered about that myself, especially since Kohler brought the "S" back on the Quiet Line wide frame AQS series engines. I had thought possibly it was due to Kohler "including their own integrated starter with the ring gear flywheel." This all falls under the FWIW category - and for what it's worth, it does sorta help to identify whether you have an original or replacement engine (or at least the flywheel shroud). It might be worth noting that the narrow frame tractors also all had the metal ID tag on the flywheel shroud while the wide frames like yours, had a sticker decal ID.
With regard to your engine starting easy and having alot of power, well wait till you get your 1650 going. I'm certain you'll notice the difference. The 1650 will "not" start as easy. The integrated starter on that AQS does not spin the engine as fast as the old Starter/Generator, and it whines/whirs as well, but you'll get used to that.
And as for your smoke coming out the breather, why don't you just remove that breather cover and clean all the parts well, and adjust your valve tappet clearances, and make sure your drain back hole towards the back of the breather box is open (not partially plugged with any crud)and don't forget to get yourself a replacement breather kit with the 2 gaskets and screen, and little rubber spacer dohickey so oil won't leak all over once you reassemble, and when you do make sure you don't torque very much on that nut (basically just snug it) holding the cover on or you'll tweek it and have oil leaking past the gaskets. Your little 10hp might just stop smoking on you, and may even run a bit better and stop smoking thru the breather (but I won't guarantee it). And when you're all done you'll really enjoy getting more seat time cutting your grass since you'll get to smell those Kohler fumes awhole lot more rather than oil smoke.
(PS - Paul Bell was a little stingy on his pic of the Kohler manual page with the engine ID info. If you could see more of the page you would see it also list a year or maybe it's the decade of manufacturer based on the serial number break down, which could also help you verify your engine may be original, or was built close to the same time as your tractor build date. Now don't get me wrong, I'm not complaining about Paul at all. He provides a wealth of info of great value to us all. It's really more of a situation that if you ask the right question you'll get the right answer details - thanks very much Paul, for everything you provide to us all).