"Then I swapped to a ditto parent plus a female vulpix with everstone, and checked both everstone and ditto parent in RNG Reporter. Now the shiny frame was 128, and I did get a shiny when I hit 128, but the nature and dream world ability was not what RNG Reporter said it would be."
You're using an old version of RNG Reporter, aren't you. If one parent is a Ditto, the baby will never have a Dream World ability. If you had been using a newer version you would have seen this reflected in the list (older versions didn't).