A new piston and rings in a untouched cylinder is a problem. Your engine is in excess of 30 years old, the wear on the engine was not only to the piston and rings, but more so to the rings and cylinder wall. The movement of the piston in the cylinder creates an out of round cylinder in the course of many years of use. It gets both out of round and tapers, by installing new rings you do slightly improve or actually reduces this clearance between the rings and cylinder, therefore increasing compression, but the new rings are round and the cylinder is not. In many cases installing new rings will snap the connecting rod as the increased pressure on the old rod and pin are substantially increased. That said, I would surmise that if your engine still contains the balance gears and was not rebuilt to standard, it is time to invest in doing so. The Kohler k341 is not as abundant as the k321 or k301 and if you want to keep it it around specific steps must be undertaken now that will prevent catastrophe in the future. Previous owners may have been penny wise, but pound foolish or relied on the advice of someone with no horse in the race, but if you find yourself in neither position, it is up to you how to proceed from here. I would start by realizing the engine was not brought to standards when worked on in the past and rectify that by doing so now. When you have the engine out, start by micing the cylinder wall and go from there. Remember measurements must be taken at the top, middle, and bottom of the cylinder. BTW, advice like this is why I have had problems on other forums, I say things some people would rather not hear. I hope you you hear that I have only good wishes for you and your engine. Good luck