It looks like you have a couple of coils there with darker wires than the others. This is a sure sign of excessive heat exposure and wiring that is "worn out" (for lack of a better term). There does need to be some accounting for age & use, but basically, you want to see a relatively bright sheen on the copper. Is the other stator you bought in similar condition?
Also, do you remember when you
first took it apart if there was an oily film on the stator and flywheel? It looks like the oil seal might be leaking, and if so, the rotation of the shaft may be throwing oil all over the stator and flywheel - that's going to cause a lot of uneven heat distribution when the engine is running. It likely won't cause immediate problems, but over time it will wear out the stator.
Have you checked the stator(s) for short to ground? With your meter set to ohms, place one lead of the meter on one of the connector pins and the other lead on the steel ring in the middle of the stator (where the screws thread through).
In theory a short to ground will cease all output of the stator, but electricity can do some really funny things, however unlikely they seem.
My final piece of advice would be to buy a new stator. It seems likely the stator is the source of the problem, and the used one you bought was simply as worn out as the one you already had.
Here's a video that goes into a decent amount of detail regarding small engine stator operation and testing. It's not a Kawasaki, but again, the principles are going to be the same:
https://www.youtube.com/watch?v=G_7FD_ZhKSg