I leveled five pokémon with Pickup to level 81 or higher, high enough that Leftovers can be picked up. I was running around in the grass on route 7 to trigger Pickup before realizing "With my luck, I'm gonna find a shiny before I find Leftovers. And Volbeat and Illumise appear on this route. I'm not having that."
So I changed locales and adjusted my luck, chain-fishing and Leftovers-hunting at the same time. And I was right.
Shiny Poliwags chain-fished: 4
Leftovers Pickupped: 1