I know you have 6 of these in your house, but I would just replace them. Old Kohler is expensive to repair and a ton of the aftermarket parts are horribly made and by reading your last post, you are figuring this out.. Weird things happen with aftermarket parts on Kohler toilet.
I always recommend 2 piece toilets, but if you like your one piece Kohler has made some great changes to new their one piece toilets and they are not hard and expensive to fix now. Bit the bullet and upgrade. You will be happy for another 15-25 years instead of trying to fix these every year.