First off, be absolutely certain you want to mix original characters and established characters. I'm not saying I doubt your writing ability, as I have never read anything you've written, but make sure you know what you are doing. I have seen mixing original and official characters work... twice. One was written in a unique dairy-like style, and it involved May and an OC developing a complicated relationship. The main reason it worked for me was the complication. If your OC is straightforward about everything and never has a conflicted emotion, you don't have a character.
But I'm getting off-topic. From my first impression, this sounds like a standard, Gary Stu author-insert journey fic. Reading on, though, it seems like you are aware of this potential issue. You even offer up that you may never have your protagonist actually defeat his rival. That's a good line of thinking to have.
Continuing what I was getting at before, you have to make your characters complex. That will be what you need to work on to make your ending plausible. You have to expose Barry's weaknesses to the reader, at least, if not to your protagonist. Also, in my personal opinion, there aren't enough small victories in fan fiction as a whole. As another example, I once read a fanfic that ended with the protagonist losing a major tournament to his idol, and then later winning a rematch in private, earning the respect of his hero, which was all he really wanted all along, not a title or trophy. What I'm getting at is that I've read a lot of fanfics, and the best ones usually don't have a happy or tragic ending. There's something I once heard: The best stories are written on middle ground. It's something that's stuck with me. Without power shifts, conflicting emotions and morals, and riding that line between tragedy and comedy, there is no excitement.
If you build up in a believable way, and have Yuki learn and grow, as well as make Barry a real, complicated person and not a faceless, infallible champion, then your story can end how you see fit. You shouldn't decide to do something just to avert a cliché. Play the battle out in your head, without deciding who you want to win. Play through every scenario, and assess all the potential outcomes. In the end, you should know what outcome would be the most entertaining, and that's what you write.
"Rampardos is unable to continue! The winner of this battle, and the Coal Badge, Lucas!" yelled the announcer [...]"
...or something to that effect. Unending, repetitive battles are no fun to read. Though, I would definitely encourage showing both battles, but not consecutively. Have a little side-plot between them, or something. If you make them different enough that it doesn't feel like the same battle played over with a different name, then it's definitely the preferable solution.
Detail is always your friend, though. Always. Just be sure to make those details fun to read.
Good luck. Also good luck in reading this incredibly-long thing. Also sorry if it got less helpful near the end, I've been typing this on-and-off for about 2 hours.