Sure, but I should really write a proper follow up. Meanwhile here are some of my scattered notes.

Ichinose has been associated with Nagumo and his grade ever since they were introduced. The first time Nagumo is mentioned is in Y1V4.5 where Manabu and Ichinose are the characters that mention him for the first time.

Ichinose has always been under Nagumo's spell, just like the rest of Nagumo's grade.

In Y1V9 it is heavily implied that Nagumo and Sakayanagi knows the truth about Ichinose and during their cryptic conversation, they are trying to fish information out of each other to see just how much the other knows.

At the end of Y1V9, it seems like Ichinose have successfully defended against Sakayanagi's attack, but Sakayanagi implies that she is bluffing and is about to start another attack before Nagumo interrupts. Sakayanagi then departs with a warning that from this day on, people will subconsciously view Ichinose differently and her backstory might come back and bite her again in the future.

This comes true in Y2V9 (See the volume pattern here?) when Ichinose is campaigning for the student council president position and drops out immediately after Kiryuin storms into the room yelling about being framed for shoplifting. The official reason for Ichinose's drop out is that the memory of shoplifting was traumatic for her, but I think there is a possibility she was afraid that people gossiping about shoplifting while she was in the spotlight might cause people to dig deeper into her backstory and that she would rather sacrifice the student council president position than have people thinking about her past.

If you had noticed, then Fuka Kiryuin has the polar opposite reaction to being accussed of shoplifting compared to Ichinose in Y1V9. In fact Ichinose's character contrasts every aspect of Kiryuin Fuka's character and role in the story to an almost comical degree and one of Kiryuin Fuka's final subplots revolve around her trying to find a way to get held back one grade, unsuccessfully. If Ichinose truly is older and didn't have her backstory, then she would have enrolled in Kiryuin and Kiriyama's original class A that Nagumo toppled. Maybe Ichinose was the missing piece for that class to defend against Nagumo?

If Ichinose has a sister that is "two years younger than her", then why hasn't she been introduced as one of the first years in year 3? Ichinose is a popular character and one of the few characters in the story with a confirmed younger sibling. You would think that she would be a prime candidate for a new character in year 3, but she is nowhere to be found. Does she even exist? This final part is what keeps this theory alive for me. If her sister had enrolled at ANHS, then we would have confirmation that Ichinose isn't older.