PokemonGUI only shows bars for pokemon near the Player prefab. HpBars should stay up to date as pokemon health changes (damage or heal).
PokemonGUI and BattleTarget should stay synced together.
Attached PokemonGUI to all pokemon.
Tweaked PokeCenter to heal everything, which avoids some bugs for the time being.
Removed Find from PlayerSave, as per Reub's insight.
I managed to break TrainerAI again, so I fixed it again. They should throw pokemon, instead of tweaking in the corner.