All done. I barely had enough viable (able to breed, and discounting trade evolution) Pokémon in my battle set to breed up the 72 we needed. It took all of my viable Pokémon with only like three exceptions, and Eevee. I wasn't sure how many Eevee to breed, so I was delaying it until the end, and I just barely squeaked by without needing to breed them.
If we get another player, I'll breed up the last few Pokémon and a couple of Eevee to fill up the total. If not, I'll probably offer an Eevee to the winner, bred for competitive IVs, Nature, and Ability to match the Eeveelution of the winner's choice.
EDIT: I do have a few more viable Pokémon than I originally thought. I SHOULD be able to cover one more newcomer. So Eevee will remain the prize Pokémon at this point.