This showed up in my "Unread's" today. I don't know why I didn't say this before and I don't know if I mentioned it in that "older thread" or not so I'll mention it here because I, personally, think it's an important thing to consider.
When I first started out with my birds I had several green egg layers. I mean more green than blue. A couple years into breeding I had 2 BW hens that laid white eggs. One had a VERY light blue tint to it but for all intents and purposes one could call it white. I used those hens to color test my roosters.
By "color test" I mean to cover those two girls to see what their pullets laid. Not knowing a thing about whether the rooster had anything to do with egg color it was just something I tried. I remember one of those roosters produced a tannish looking egg. That told me that he was passing on what I call "brown egg gene modifiers". I honestly don't recall if I came up with that on my own or whether I saw someone else say it.
All that is to say I'm pretty sure the rooster plays a part, I'm guessing 50%, in offspring egg color. Part of my breeding program is to develop a "stud". A cockbird that I can keep for years to then linebreed successive generations of females. Of course, I would keep a female if I got one that was exceptional but my goal is to get an exceptional male that I can cover numerous females with for years. Then no more feeding males until they're a year old to see whether they're a keeper. Unfortunately I'm not quite there yet. However, there's always this year!
So all that is shared just as something to consider if you haven't already.
One other additional side note. All this brings up the importance, once again, of evaluating your birds and then putting a breeding plan together - I recommend a 5yr plan - that prioritizes what traits you are attempting to "fix". By that I mean "fix" as in "set". Ya just can't fix everything at once. Personally, I've not prioritized egg color as the judges could care less about egg color and from what I've read nobody is still, to this day, even sure what all is involved in egg color. But, if your goal is to get the bluest eggs I think John's advice is spot on. Breed the bluest to the bluest. Make that your #1 Priority in your Breeding Plan and toe punch accordingly.