Haha, now that part is just sleight-of-hand. When you click (technically, mousedown) on the google doc link, we copy a new item to the pasteboard, so now instead of {"html": joker_image, "plaintext": card_you_picked}, it's {"html": joker_image_with_url_paste_hint, "plaintext": twitter_url}.
For how you can save multiple mime types in the same paste entry from javascript, the w3c draft is: https://w3c.github.io/clipboard-apis/#clipboarditem