On a sort of different note.. I never cook my chickens at that low of a temperature. The whole "low and slow" thing is great for large chunks of tough meat to slowly break down the connective tissue and make it super tender. But with chickens.. you're not trying to break down connective tissue. You're just trying to infuse smoke flavor to a roasted chicken.
So when I do mine, I do them at 400 degrees and I smoke them during the cook time. It's basically the same way I cook them in the oven, only with smoke. Skin comes out crispy, meat is nice and smokey, and I've never had a problem with the red.
Doing it beer can style works good to, because you have an additional heat source (the hot water) inside the bird. So you're cooking from both the inside and the outside, plus you're adding steam, plus you're adding smoke.
My .02
Good luck