The only out going calls that affect the Shiny Egg part of the breeding process is Joey. Any incoming calls by anyone, affects it badly. So you want to avoid getting any of them.
If you do happen to get a call before the daycare man has the egg, it's most likely not going to work, and you'll have to restart.
Irwin calls will not affect your shiny egg, just the IV's it will get. Since you're just going for the shiny part, you won't need to worry about IV's just yet.
Don't bother ditching eggs, unless if you have an even frame for the shiny egg.
As your process can be severely eased by doing 1 thing.
So if you're wanted a frame 3 egg, you call Joey once. It advances the shiny egg frame by 2. So than your egg will be that of frame 3.
Just make sure to call Joey before the egg is produced by the daycare man.
Also, the reason why you might have gotten to frame 4. Did you receive or send any phone calls while you were throwing eggs away?