You need points to last longer than 40 years?
We all know what the Kirk "transdenser" does, we don't need a lesson, but thanks. Some on here have used them, several have had issues while using them. Those of us who have "been around" and know how to time and tune these engines agree they are a waste of $40 (or whatever they cost now). Believe us, me, George and others when we say they aren't worth it. It isn't an electric ignition conversion. It doesn't replace the points with a PIP sensor, it just lowers the amperage to the points and allows you to run a slightly hotter coil, but only by maybe an OHM or two. Hardly worth the trouble.
On tuning carbs... yeah, we've done a lot of that too. Don't use the "factory" setting. If you read the manual exactly, it clearly states the recommended setting to be used as a starting point to tune. You can't really read in a book how to tune a carb. It's more of an understanding of the engines reaction to the setting. As George said, you need to err on the side of rich. It's far more likely the PO just didn't know how to tune it, than it is that he had it set for winter. I seldom change my carb settings in the winter months. And we have temp swings between summer and winter of up to 115°. Do read the manual on carb tuning, it does a pretty good job of explaining it. Start by setting the idle stop screw to just contact the throttle plate stop. Adjust the low idle mix screw and the idle stop screw in increments together to obrain the low idle mix. A K341 has a good idle spot where it runs pretty smooth. Find it. It will not be at the speed the book suggests.
You will need a tachometer of some kind to set the high idle, no load speed. Then, adjust main fuel after that speed is obtained. Double check both low and high idle speeds and settings when done. Tweeking will be required.
Once you throw away the Transdenser, get a good condenser, set the timing and tune the carb, it should fire in no more than two revolutions. More if it's really cold out.... maybe 4 or 5 revolutions.
If you want electronic ignition and EFI, Kohler does offer those in their new engines.
You are welcome to read the Kohler manual on static timing. Or you can use this:
https://www.onlycubcadets.net/forum/...ad.php?t=33461