Solved in a real browser.
Every token is minted in an actual Chrome, with the widget loaded on your target’s own origin. Nothing is replayed and nothing is forged, which is why the token behaves like one the page minted itself.
The checkbox gets clicked, the challenge gets read off the live page and answered, and the token comes out of the widget callback the way it would for a person. One task covers the whole sequence, however many rounds it runs.