I followed the Brewer diet pretty faithfully last time around, and have just started to pick up on it again. This isn't my typical way of eating, so it did take a bit of adjustment, some calculating and planning. I did feel like I was eating a lot, but gained about 35 pounds, which were easily shed. DS was born at a good weight and was healthy as can be.
My secret snack were these grocery store bagels, I think they were Thomas' 100% whole grain, they're decent enough, but they pack a surprising amount of protein. One of these with some peanut butter and fruit, or made into an egg salad or chicken sandwich with greens and shredded carrots really helped me keep up my protein intake and check a few other boxes off of the list at the same time.
I'm pretty averse to milk this pregnancy (still??), so I'm running into the issue that you've got... so far I try for a bowl of cereal a day and do the best I can with cheese and yogurt. I just drink grocery store organic milk, I don't have easy access to raw milk, either.