I'm not sure what the grey silkie diluting gene is. I think it's lavender so really you don't want to do a lavender and blue dilute breeding I think. If you do you would get:
E Lav
E. EE. Elav
Bl. EBl. Bl lav
So 25% black, 25% blue, 25% lavender, and some kind of crazy over diluted something in last 25%.
Might be worth doing just to see what a bue lavender mix looks like. Maybe.
Anyways, I don't think I was much help but that's my two cents?
Breeding Lavender into your BBS colors is pointless, as it wont show well, except in the feather structure. Just muddies the water. If you are going to start mixing genes, have a plan in mind of what you are trying to accomplish, and what your goal for doing so is.