Here are some "Boy, is this ever stuck!" ideas:
Can you download an exploded view or a parts view for the faucet? It'll help you figure things out. Perhaps there is an e-clip or similar under the translucent disc with the writing.
Maybe a gentle attempt at rotating the bonnet will break it free. Caution- Go gently so you don't break things.
Possibly lime built up inside & is holding the parts together.
Cover anything below that may be damaged by vinegar. Wrap a cloth soaked with vinegar around the seam and wait perhaps a day. A gentle tap an hour or so after placing the vinegar may help work the vinegar in. Hopefully this will work well for you.
Is there a way to use a rented faucet handle puller or a gear puller? Work gently so nothing breaks.
If you have time to be on hold, perhaps calling Kohler technical will provide a solution.
Paul