It will be a little difficult as the two colors (blue and Lav.) can be challenging to tell apart to many people. But it's really not that hard excepting very light blue Blue birds will look like Lavender. That said those birds are poor examples of Blue color so would be culled out with lavender birds anyway.
The standard for Blue is slate blue or another way to visualize it is Pigeon Blue. Lavender is dull grey, no two ways about it. Poor Blue color can look like that hence the difficulty in distinction. What I was saying is Blue has lacing or edging if you will on feather tips. Lavender does not. The standard for all Blue is for lacing and this variety for all breeds needs improvement in lacing. Going forward always use Blue with as much lacing as you can get and that guarantees you are mating Blue.
As for the genetics of what's going on you are starting with Lav and BLue. Lav gene requires both loci to be Lav to express. Blue varieties hatch out Black (no Blue gene), Blue (one blue gene) and Splash (two blue genes). Your F1 generation, first hatch from this pairing, will hatch out 50% black birds and 50% birds expressing blue. All of them will carry one gene of Lavender meaning they are split for Lav.
Mating the best laced blue birds of F1, don't use the parent cock as you feel his body type is lacking, will beget F2 generation. As each F1 bird carries one copy of Lav this will result in 25% offspring carrying no Lav, 25% will express Lav as they have two copies and 50% will still be split for lavender- carry one copy of gene. As you can see it's going to take generations to weed out the Lav completely. But by F4 generation you'll have keeper birds from previous generations. with test matings you'll be able to determine who is carrying lav and who is not. I'm confident you will eliminate that gene from flock in at most 5 generations.
BTW, that K (cockerel) you were holding in photo is Blue. I saw a splash in a photo too. Are any of those birds in photo suppose to be Lavender? I don't see any.