There's a couple of issues I can think of when changing your character. You probably have the other character model actively loaded which will cause the screen to not even boot up properly. Also, the separate characters use different flags for events and can cause some misses when doing completion checks.
The second issue cannot be easily overcome, but it is less of an issue (the game might just nag at you). The first might only be doable in very specific cases like right after saving after beating the champion, modifying your save, then loading your game. It still might not work, but it's worth a shot.