It's also possible that Naruto uses his strong willpower. We know Naruto has an unbreakable spirit. He could use that determination to resist the effects of the seal until it eventually breaks. He might enter a state of deep meditation or concentration and focus his chakra in a way that overpowers the seal.
Kakashi could also be of assistance. With his Sharingan, he might be able to analyze the seal and figure out its weak points. Then he could guide Naruto on how to target those weak points and break the seal.
On the positive side, new and better policies could be implemented. If the old council was corrupt or stagnant, getting rid of them would open the door for fresh ideas and reforms. Naruto could bring in new people with different perspectives to help run the village, leading to a more prosperous and fair Konoha.
In a fanfic, if Naruto's seal gets damaged, he might lose control over the Nine - Tails' power. This could lead to sudden and uncontrollable outbursts of chakra. For example, he could accidentally harm his friends or destroy the surrounding area during a fight.
He might use his influence as a hero. Naruto has a lot of friends and supporters in the village. By getting them to see his point of view about the council's inefficiencies or wrongdoings, he could start a movement to oust the council. For example, he could talk to his old friends like Shikamaru, who is intelligent and might be able to come up with a strategic plan.
One consequence is a change in his physical strength. Kurama provided Naruto with a huge boost in power, so without it, he might not be as strong in terms of brute force. However, this could also force him to become more strategic in combat.
Jiraiya is another character that could be present. As Naruto's mentor, he would be concerned about Naruto getting the cursed seal. He might try to find a way to remove it or at least teach Naruto how to manage it without losing himself. Jiraiya's vast knowledge of ninja arts could play a crucial role in Naruto's struggle with the cursed seal.
If Naruto gets rid of Kurama in fanfiction, one way it could change the story is that Naruto would lose a major source of his power. He'd have to rely more on his own natural skills and training. This might make him seem more vulnerable at first, but it could also lead to him developing new and unique abilities. For example, he could focus more on his Sage Mode training and become even more proficient in it without Kurama's chakra interfering or overshadowing his progress.
Kakashi could play an important role. As Naruto's former teacher, he would surely want to help Naruto understand and control the Caged Bird Seal. He could use his knowledge and experience to guide Naruto. Another character could be Jiraiya. Even if he's not alive in the original story at a certain point, in the fanfiction, he might return as a spirit or something to give Naruto advice about the seal.