Adam, I agree that you should be able to pick Zack up without him growling. Zack is a border collie, right? I don't know much about BC temperament. I know they are highly intelligent, have lots of energy and need lots of exercise.
I have a new puppy too. He is a hound mix. He growls a lot. He growls when he plays with other dogs and when he plays with us. I don't have a problem when he "play" growls. But, like Zack, he also growls when he doesn't like something. He never growls at my husband or me. He growls at my kids - who are young adults. My puppy does not like to be picked up, made to go in his crate, or stop doing something he wants to do. He will sometimes growl if my kids try to "make" him.
msvette gave me this link to mind games....
Mind Games (version 1.0) by M. Shirley Chong
I have been using mind games and it is really helping. I am seeing much better behavior from the puppy. We also try to desensitize him to the things he doesn't like. He is by no means a nasty, or aggressive dog. He has a wonderful temperament. I just find the "I don't want to do something growling" inappropriate.
I believe the reason he growls at the kids vs me, is because they do not approach him with confidence. They were also not incorporating the rules. Now that they are listening and we are all on the same page.....HUGE improvement.
Zack should be handled every day. Look in his mouth, ears, lift his paws. Touch him all over. Like doggiedad said, "make picking him up part of his training routine."
Good luck and keep us posted!