I think I see the problem. I thinking it is one of the CV16-FHP engines which uses the 12 584 17-S coil which looks very much like the Tecumseh coil in my previous post. Notice the distance in where the mounting holes are when compare to the one you currently have on the engine.
Also here is an image of CV460 that uses the 12 584 04-S coil.Notice the flywheel magnets are mounted differently than the one you have. It is right inline the ring gear teeth tips. Your flywheel has it recessed.
View attachment 62624
Very interesting as that was not what Kohler listed as an engine option. They could have been very wrong. I don't remember the exhaust looking the way the parts diagrams show (I can't look right now). I see what you mean by the flywheel teeth and the magnet mounting. The coil that came out though was a Tecumsah based on the part number on it. I'm thinking that somewhere in the past, someone couldn't figure out what coil to use since they didn't know what engine they had and found the Tecumsah the closest in appearance. Which brings me to this question:
Should I:
1. Get another Tecumsah coil
2. Try the coil you suggested, not knowing whether it will work
3. Redrill the Kohler coil so it fits
Also, I noticed the parts lists talk about DSAI. My engine had what was listed as #23 in the following diagram(
https://www.jackssmallengines.com/j...hp-16-hp-11-9-kw/ignition-electrical-5-27-174) but didn't have #9. I assumed that #23 was the rectifier, which I just swapped out with #9. When I say I had part #23, it was the square thing in the drawing (not the part shown for 23)