Not positive for all production but they were used in the Power king tractors from 1979 thru 1984, so that is 6 years. They were used in Simplicity/ Allis GT's, and maybe others. They are a smooth running with good power and torque. There are a number of reasons for the problems they had and the problem was they dropped valve seats. One of the reason (maybe the main one) technology at the time, dropping valve seat is not a Kohler problem only the OHV Tecumseh had the same problem, Over heating of the cylinder head caused the seats to drop this was, over heating had a number of causes 1 the cooling fins were somewhat limited do to the OHV assy, 2 the first gaskets between the head and the valve assy were not good and let oil leak onto the head and cooling fins baking on a build up of burnt oil this really reduced cooling 3 grass and other debris would stick to the oil and further reduce the cooling even the cylinder barrel fins. Another but nearly as serious is that the valve lash seems to need to be watched closer .
The need for more maintenance is required to keep the engine going one is don't let it leak oil all over the head and cylinder, 2 clean the cooling fins head & cylinder regularly keep all the factory cooling tines in place also these heads have a steel insert in the exhaust port its required some guys that like vertical exhausts remove them or don't know what it is and remove them when replacing mufflers etc.
Now as for repairs these heads are easily repaired by a good automotive machine shop ( a billet head is not needed in fact they are for pullers not every day use), auto machines now have the means to repair these as its not a problem for only small air cooled engines many car engine had the same problems when mfg started using alum for heads so machine shop have seen and know this valve seat problem.
Some guys change the seats to bronze and they will hold but I'm don't know about the longevity of a bronze seat for everyday use.
And lastly the problem now is there are no new heads available and some heads are damaged to the point they can not be repaired so finding a replacement head can be hard and expensive
Hope this helps clear up some of the misconceptions about the K361 if maintained its as good an engine as any of the K series