Your first cross will get offspring that have a split blue/white egg shell gene, blue is dominant and will be expressed in all first generation birds thus all will lay a shade of green due to the brown overlay being introduced... What gets complicated is that this first generation will also have a mix of 13+ genes that control the brown overlay color and intensity, this brown 'overlay' pollution and the high number of genes that create it is where the unpredictable mess begins for color... Second generation chicks would return to brown if they get a double white shell gene, but it would likely be a different shade of brown likely lighter pink or orange (but not always) since the cluster of brown genes was diluted... Lots of variables when you have 13+ genes determining if the egg gets the brown color, to get back to a true blue color you will have to breed until all those 13+ genes are turned off...
From this point it's pretty easy to breed out the white or blue egg gene to breed true, but it's going to take a lot and I mean a lot of trial, error and culling to breed out the 13+ brown overlay genes to return to a true blue laying bird again...
FYI I have yet to see a Whiting True Blue egg in person, but the pictures online suggest that there is already some pollution of the 13+ brown genes thus giving the 'mint' green overtones to their eggs vs the bright sky blue seen in the original blue laying breed(s)...