It sounds to me like it's the milk, and you see the connection yourself. IMHO, children's need for plain milk is VERY overrated. A person needs 2-3 servings of dairy each day--they do not have to be plain milk. And technically "servings" of dairy are quite small. A "serving" of cheese is 1 inch cube. A 1/2 cup of yogurt or cottage cheese is considering a serving.
When given the proper nutrition, the body will poop just fine on its own--no medication needed. Dairy and processed foods are the #1 culprits when it comes to poop issues. "Processed foods" being things like boxed mac 'n cheese, Hamburger Helper, frozen pizza, potato chips, and so on. It doesn't matter if it's organic or "natural"--processed food is processed food.
If this were my kid, I would go back to your original diet of OJ and very little milk. Encourage him to drink more water. When diluting his juice, you can add more and more water. We had to do this with my son, and now he drinks water just fine.
Push fiber rich foods like: oatmeal, whole wheat anything (pasta, bread, crackers), fresh fruit and vegetables, nuts, raisins, and dates, to name a few. Flax seeds have an incredible amount of fiber in them. They can be baked into breads and muffins, and sprinkled on oatmeal and other cereals. Good luck.