Basically, I want a team that uses only Delta Pokémon and Mega Eevee. I want this team to be able to get around the middle of the game.
Look the answer to the similar question here (info on Delta team and on step-by-step availability):
Winning Elite Four at Hard with Delta only is more than possible!
Delta Snorlax, Delta Haxorus, Delta Scizor (or Delta Scyther), Delta Gardevoir/Delta Gallade, Delta Roserade etc (look above for good setups).
Information where to find them:
https://wiki.p-insurgence.com/Pokémon_Locations