I have been a Great Dane owner for the last 15yrs and a rule is no puppy food for Dane puppies as puppy food pushes their growth, which is something they don't need.

Does the same rule apply for Berners? My pup is 9wks. He was a pup I fostered. I fostered his mom and littermates, and had to feed Science Diet because that was what was required. Now that he is ours I have switched him to Diamond Naturals. We used to feed Taste of The Wild to our Danes but they were actually loosing weight on it. I have fed raw in the recent past also but I have a picky eater (Dane) and she was refusing it. So I have my Danes on Diamond Naturals Chicken and Rice and the pup on Diamond Naturals Lamb and Rice Large Breed Puppy. I know your not supposed to feed Lamb permently so I thought I would gradually add the Chicken and Rice Adult food until he was switched over. Does this sound ok to do?

My vet wants to weigh my 3 month old at 4 months and then maybe switch to adult food.

Low protein content in their food is a good idea and puppy food usually has a pretty high protein content so I would stay away from it.
The reasoning is you don't want these guys growing too quickly, it's hard on their joint and bones.
Keeping them slim is also a good idea, just enough so you can feel their ribs.

Good luck!

I would go with a high quality food made specifically for large breed puppies. The most important reason being is that the calcium/phosphorus ratios are balanced for the rapid growth of large breeds puppies. It is a myth that large breed puppies should have restricted protein. They need high quality and adequate protein for proper muscle and soft tissue development. What large breed puppies do not need is too much calcium and adult foods are usually too high in calcium. Too much calcium makes the bones grow too quickly and is known to cause certain disorders such as OCD.
No matter what brand of large breed puppy food you choose, it is very important not to over feed. I believe that is one of the major factors in growth issues in puppies. A slow, steady growth is best. A Bernese puppy should grow at the rate of about 2-2.5 pounds a week or 10 pounds a month. Growth that is much faster than this is likely to cause bone and joint issues later.
Dont forget to give your puppy plenty of free exercise time as well. Exercise is important in allowing those muscles and bones to grow strong and healthy.