Even if you gain weight, with all the body weight stuff you are doing, it is guaranteed that you won't put much muscle.
So when you cut down from 250 back to 220 or 230 whatever, you won't look anywhere close to what you are expecting.
The whole point of bulking up is to put on as much as muscle as possible. Not to eat a lot of food and get fat and cut back.
An it is not about milk, it is about getting as many calories the easy way. When eat that much food, protein intake is the least thing to worry about. You will get enough and more.