Well, I have figured out how to edit the level... but it's probably not what you wanted!
The character's base stats are not changed until the next natural level up (which of course is now even more inconvenient, since it will take an unrealistic amount of experience to reach how much you need to normally be 71)
I have tried to figure out where experience is stored but didn't have much success. Haven't tried the stats yet but it probably won't be too fun either.
Here are the addresses anyway, since there's a huge lack of documentation:
#84: level on save screen
#F8D0: Shulk's level
#FBD4: Reyn's level
#101DC: Dunban's level
#104E0: Sharla's level
#107E4: Riki's level
#10AE8: Melly's level
After editing levels, the game may crash when the team appears on the bottom screen. In this case, mash X after loading the save and get into the character selection screen ASAP, change the team, exit the menu, and if it now works defeat one enemy and save!