You know, I realized I was wrong. There doesn't seem to be any way to get a Pokeball off of a Pokemon into a different species period. It doesn't matter which egg group it is.
If you had a female Rattata in the ball, that ball would be passed down to a Rattata, because you will always get Rattata eggs from a Rattata mother.
If you had a male Rattata in the ball, you can only pass down the ball by breeding with Ditto. And when breeding with Ditto, obviously you always only get the Pokemon that the non-Ditto parent is.
It would be possible to move balls onto another species if the ball passed down by the father (when not breeding with Ditto), but since they locked it to the mother, you can't. Sorry I confused you. That would've been great, huh? Definitely makes it more annoying that the apricorn balls are so hard to get since they did it the way they did.