I only learnt about the Joey calls thing the other day, so I've never actually tried it with those.
Here's what I'd normally do:
Open RNG Reporter, click on Time Finder, click on the Shiny Egg tab.
Fill in all the things I want, like nature, ability, etc... And click on HGSS Shiny Egg (and international parents, but that's only if you have them).
Click generate, and then find one which is on frame 1.
If there isn't one, I just change the date, and keep doing that until there is one on frame 1. I don't really know about the Joey calls, just repeating what it says on the first page.
Feel free to message if you need any more help, always glad to be of assistance :)