Oh no! You have to resort to a strategy other than using overleveled Pokémon, what a nightmare!
You've never had an issue with your Pokémon being overtrained in any other games because all those other games aren't like Pokémon Reborn. The entire point of the level cap is to cause you trouble.
While we're on the subject, I want to address something that has been bugging me for a while.
Common Candies make the game a lot easier than it should be. If one of your Pokémon exceeds the level cap, all you have to do is spend $300 and the problem goes away. If you overlevel a Pokémon, you should either box it or drop some serious cash to buy back its obedience.
I think it would make playthroughs a lot more interesting, at the very least. If something becomes too high-leveled, you could box it and replace it on your team with something else until you raise your level cap. Forcing players to adapt and innovate is something that Pokémon Reborn strives to do, and I think the scarcity of Common Candies would complement that well.