I know you mentioned (many, many posts ago) that this method didn't work with genderless pokemon. My understanding is that it does work, but you have to either reject the first egg produced or reject every odd egg (1st, 3rd, etc). Maybe I'm wrong, though, the egg swap method is the only legit shiny hunting method I haven't done yet, I've just read the guides.
Ok, so I just tested this with Beldum a few minutes ago and it actually did work. All I had to do was reject the first egg that the daycare lady tried to give me and after recieving the next egg, it hatched a shiny Beldum!
Thanks for the tip! Apparently this is how it works for Genderless, and only Male/Female pokemon.
I'm glad it worked. I've got a couple of genderless pokemon on my long term list, so I'll have to figure that out for myself as well. Thanks again for the Froakie, my girlfriend is super pleased and slightly more trusting.