As for ideas for BP rewards, I have a few if that may help you. 1. A grooming service to raise friendship to the max value (255), mainly for return or evolution purposes. 2. Galarian Pokemons, if you're willing to add them there instead of Mauville. 3. Items to make the unused/unavailable legendaries spawn where other legendaries currently appear at, or other remote locations (Ashenwoods, Petalburg woods, Shoal Cave, New Cave inside Victory Road, Mirage Island, Dewford Manor, Event Islands, Artisan Cave in Battle frontier, Team Aqua/Magma lairs, Top of Volcano, outside the Sandshrew ruins, Safari Zone, Mt. Pyre, etc.). 4. Masterball (slightly less useful but still an opportunity to get more than one). 5. Mirage Island guaranteed day or permanent/togglable access 6. Egg moves tutor. 7. Turn a Pokemon shiny OR shiny charm. 8. Ability to own both bikes? 9. I don't know since it's Emerald, but E-Reader berries and RegiDolls. 10. Turn your secret base into a bigger one (would need to create a new location probably). 11. Cheaper EV trainer (50k for one Pokemon is on the expensive side). 12. New box backgrounds 13. Ability to buy berries 14. Ability to set your level or rare candies.
As for Bad eggs, will they only appear in box 3 and 6 like it often happens?