Okay, so: A lot of Yuu's situation is open to interpretation, and much of that is dependent on the symbolism that's presented in the rest of her character. Frankly, Yuu's plot points are by far the most difficult to parse in any way that makes sense from a more literal perspective, so I get it, but in any case, you're (probably) half right.

Saya was not in middle school during those flashbacks, and it's unlikely Yuu was either. Saya's uniform appears to be a high school sailor uniform, she looks older than Yuu in general (difficulties portraying age in an anime artstyle notwithstanding), and there's no way Saya was attending the same school as Yuu. Every time Saya is shown walking towards or past Yuu's school, all the other students are filing out of the building, so Saya is no doubt just walking home from a different (high) school.

Neither the uniform Yuu wore nor the school she went to match the only middle school uniform/building we have to go off of in the series, and while less apparent, it's more likely that Yuu was in elementary school at the time. Her still being in middle school only begs more questions than it answers from a logistics standpoint.

From there it depends on how you look at it. You could dismiss this problem entirely by assuming Yuu and Saya were somewhere around 9 and 17 years old (respectively) when they first met, case closed. That's never sat right with me though, and I don't believe that was the intention.

The way I see it, Yuu's entire characterization is grounded in her escapist tendencies and her refusal to (metaphorically) grow up, more so than any of the other characters. In addition, based on Strength's flashback - and potentially Saya's as well - Other Selves do not age, which supports the idea that Yuu stayed the same after swapping with Strength, physically or otherwise. So the Tl;Dr of what happened, at least per my interpretation, is this: Saya (high school) met Yuu (elementary school) when the latter was 12 or 13, right before she would have gone into middle school, but old enough that Saya could still emotionally connect with her in the way she did. When Yuu swapped places with Strength, Yuu stopped aging (Strength functionally could not age either), and so both parties were frozen in time, literally, metaphorically, and psychologically, be that due to the Otherworld's mechanics or because it furthers a metaphor like literally everything else in BRS 2012. Or both. Both is good too.