When Gary eats I just throw treats into his bowl sometimes. Yeah I have pet him to make sure he is okay with it, but I do not stroke him and sit there bothering him for a long time. Besides, when a dog eats it only lasts a few minutes so chances are good that no one will NEED to pet your dog while she is eating
For chewing, I usually give my dog a chew toy when I need a break from petting him and giving him attention lol. I still make sure he is okay with me touching his bone and taking it away. I give him a treat, good boy, and then give him the bone back. No need to pet really though.