I had a zx6 that would do this. It wasn't as bad as yours is. Mine would act up, occasionally. I fixed it, almost by accident.
I was looking through ebay and noticed how cheap relay boxes were, for specific Kawasakis . Some were 10-15.00, shipped. Others were 149.00.
I decided it would be a good idea to have a spare relay box. In my search, I noticed how there were several different bikes that used the same piece, and same part number. Mine happened to match up to the ninja 300. I ordered it and put it in the bike to test it. It worked, so I left it in. The problem never happened, again,
When you troubleshoot, it's never a great idea to throw parts at something, but in this case, the used box was so cheap, it might be worthwhile for you to try. It was easy to change (3 plugs) . Even if it does nothing, at least its a part you can remove from the list. I suspect your bike is similar, and the relay box is used in other models.