Sorry am finding it difficult to understand your explanation. I nearly get it but not quite,
You will be better going to see an advisor at the SU and make three timelines, one of which contains the events as the uni sees it, one as what SFE understand it and one in which you understand to be the situation.
Actually I read it again and think I understand it.
1. Uni kept you as October to summer intake.
2. You suspended.
3. Uni records were still Oct intake.
4. You came back and in your mind restarted uni for the opposing intake. April.
5.As the uni didnt change records then as far as they are concerned it was and remains October, but you are now on an April- start academic cycle.
1. You either suspended or you did not.
2. You were either paid for Oct or not? I am assuming not.
3. Your suspension was official and you have evidence.
4. Get a letter of confirmation from your department confirming you had suspended studies and switched to the April intake. Your department and or tutror can confirm this.
5. Take the letter to student admin or talk to them and confirm that is sufficient for them to amend their records. Imo its your responsibility to have sorted this out.
6. If they wont amend, then talk to the information commissioners office about right to rectification, that is changing inaccurate records.
https://ico.org.uk/for-organisations/guide-to-data-protection/guide-to-the-general-data-protection-regulation-gdpr/individual-rights/right-to-rectification/7. Then go back to admin and explain what ICO said as well as department.
https://ico.org.uk/global/contact-us/helpline8. If they still wont listen then make an official complaint using the complaint procedure of your uni which should be on the website. Someone independent will look at the evidence and make a decision, which if you win will force them to change the record and then you cna send the amended version to student finance.
That is how I would solve it.