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Do you have to put the bird on the grill as soon as it leaves the brine? Could you brine it for 24 hours and then let it sit in rub for 12 hours before it hits the smoker?
Think about adding the spices to the brine? You can roast the spices for more flavor, warm in water to get more flavor, add to the brine and now you have a marinade.
Keep in mind the 40-140 temp guidelines and all should be OK.
i always let something I've brined rest in the fridge for at least 12 hours, it drys the surface really good and lets everything inside the meat come to an equilibrium