What a beautiful and original piece! And sad, too, because of what really happened to Tidus.
You had an interesting juggling act to do here: you don't want it to be too Mary Sue, you don't want the focus to be on your original character, but on Yuna. Yet you've come up with a very original story, a Yevonite defecting to the Al Bhed. (I can believe that. They're willing enough to take in Summoners; they'd understand your character's misgivings.)
You might get a few accusations of Mary Sue, but I think you might be daring here and explore, a little more, your own character's story, perhaps in a different work or perhaps by expanding this one. The one nit I have to pick is that the passages about her fascinating story are so summary -- defecting to the Al Bhed, joining an alien race, being taught by Rikku, joining the Psyches when one is obviously NOT Al Bhed (maybe she's one of those who always wears a mask?) and would attract attention and scorn, living as an Al Bhed and getting picked on by Yevonites, and so on... there is so much potential for story here, dramatic moments, personal moments, that I find myself wanting you to slow down and explore her experience a bit more fully.
As long as you make her flawed and human you should dodge the Mary Sue curse. I think it might be worth doing.
Just a thought. It's a wonderful story, anyway, a unique and original perspective!