Personally, I would not cook the cheese before you put it on the pizza... I would just use a smaller amount. Fresh mozz is meant to be used sparingly, not piled on like some do with brick type mozz. I just made a 9" pizza (see pic below) with fresh tomatoes, fresh mozz (Precious in the cryo package) and fresh basil with a little kosher salt and olive oil. This was baked at ~750o F... the cheese melted beautifully and didn't water out. I have also used the BelGioioso packed in water and it melted the same way. Since you have purchased a high quality cheese, why mess with perfection? I can assure you, the professionals don't cook their fresh mozz before putting it on their pizzas.. that milky creaminess that you are trying to get rid of is exactly what they are after!
EDIT: meant to say also that on that 9" pizza, I used ~4oz of cheese, sliced thinly with a cheese wire.