Is relaying an offensive story about Allah and His Messenger—along with seeking forgiveness and laughing while relaying it, then feeling fear and remorse afterwards—considered disbelief or mockery that warrants extreme concern about the acceptance of repentance?

Narrating disbelief is not considered disbelief if the narrator did not intend to affirm it or treat it lightly. Rather, it is clear from your question that you sought forgiveness while narrating, which confirms that your narration of it is not disbelief. Al-Qadi Iyad elaborated on this issue, stating that narrating disbelief for amusement is not permissible. However, narrating it for a legitimate purpose, such as bearing witness or refuting it, varies between being obligatory and recommended. Mentioning it in the form of stories, jokes, or anecdotes of fools is forbidden, and some of it is more severely prohibited and subject to punishment. If the narrator acted unintentionally or unknowingly, or if it was not their habit, they should be reprimanded and prohibited from repeating it. If the utterance was offensive, the discipline should be stricter. If the narrator is accused of fabricating the statement or if their approval of it becomes apparent, their ruling is the same as that of one who insults himself, and they are held accountable for their words.