None of that really matters at all.
I don't think chain-hatching is a thing. The chance stays the same for any given egg (assuming you were using the Masuda method to help). If not, well, it depends on who the parents were. It's dependent on one RNG roll (it might even be done when you receive the egg, not entirely sure on that), which is independent of how many eggs you've already hatched, meaning it doesn't change based on how many you've hatched. You just have to keep hatching until you get one.
So you're not ever inherently losing anything by changing who you hatch, nor were you really building anything in the first place. If the Masuda method was used to produce the egg, or not, that is the rate that the egg will hatch. (So if it wasn't used to produce the other egg, but it was for Eevee, well then there would be a difference, but I assume you're using it on everything if we're doing shiny breeding.)
P.S. I notice you have the "chain-breeding" tag in your question. The term "chain-breeding" isn't related to being shiny, it relates to egg moves that can only be passed onto Pokemon by a father who in turn learned the move as an egg move or in a prior generation. Like getting Iron Tail on my Minccino in Generation 5 by using a TM on (God knows what that was that I taught Iron Tail in Platinum, too long ago).
