Crispy chicken skin on the BBQ
You are getting a lot of it right by patting the chicken dry and using a dry rub, I think you just need to tweak your method a bit. 

Rendering fat and making crispy skin takes time, 7 minutes just isn't long enough for all the fat to melt away and it is searing instead. When I make crispy chicken in the oven I bake it on 190&deg;C (375&deg;F) in a fan oven for 35 minutes - that's thighs and legs, breast may vary. 

What I would suggest in the barbecue is to reduce the heat to a bit short of medium, and cook the chicken longer on indirect heat. Once the fat has rendered and the skin gets crispy you can crank the heat up and get some color on it if you aren't happy with the color already. I'd keep the crispy skin away from the high heat though as it's likely to burn, instead caramelize the underside of the chicken.