Stay away from E10 for as long as you can – stick with E5 or even ethanol free if you can get it.
The ignition trigger unit that you illustrate is what is often marketed in the UK as a Nova, and it’s fine for your Kohler. I happen to prefer the Meco as it’s smaller and easier to hide within a flywheel magneto.
Assuming that your Kohler’s coil has two small diameter wires in addition to the HT lead, one will usually be the low tension lead that normally runs across the back of the engine to the points and the other may be an earth/ground. If it only has one small diameter wire, it is the low tension wire which should be attached to one terminal of the trigger unit. I don’t think that it is polarity sensitive, so its other terminal is grounded. If it doesn’t work, swap them over. I have, in the past, found that the insulation on the low tension wire cracked, and shorted out where it runs across the back of the block under its securing clip.
The trigger unit replaces both the points and the condenser, so there should be just one low tension wire from the coil to the unit – unless there is also a handle-bar mounted kill switch, which will have a connection to the low tension / module wire and a ground. If your machine has a kill switch, I would check all its wiring for shorts to ground / earth – or disconnect it – remembering that you will need to short the plug out to stop it!!
As far as your chewed up crank thread goes, I would be inclined to cut off the offending bit, counter drill and thread it to take as big a set screw as the diameter of the crank will safely accommodate. Coarse thread, big washer and Loctite !
