I heard once that neither of your dogs should be noticeably alpha. Because if one dog is alpha then you are no longer alpha. The example was...what if your alpha dog attacks you, since he is alpha the other dogs would follow suit.
If I had to pick an alpha between my two, it would be Rocco, he is bigger, older, and a male. If Maia, younger, a little smaller, female, is being cranky with a foster dog or him he holds her to the floor by her mouth. I don't make a point to feed one or the other first and they have never fought over food but neither has ever tried to take the others. I have never noticed any door blocking but I think it is because they are both too focused on getting in or out of the door.
I would think you could just let them figure things out just don't let Cooper get too full of himself. With limiting his rooms in the house and not limiting Kramers you might be helping Kramers status.
Another tid bit. With foster dogs, you are not supposed let them have free reign. Freedom in your house is earned, your own dogs have earned it. So it is not fair to let a foster dog come in and automatically have freedom. I know neither of your dogs are fosters but maybe bringing a new dog into your family is similar. Cooper should have to earn his freedom and when he outwardly dominant he loses freedoms.
Just some random thoughts.