Right around 30 a day works fine for me. You might want to read the book Protein Power, by the Eades doctors. It explains why you don't really need to worry so much with the fiber. That said, if you eat a big salad each day with your meat, cheese, etc. on it, that will give you some good fiber, as will things like the flax muffins, which are fairly low carb (I make a big one that is about 3 net carbs).

I would try to avoid famine mode with more carbs, but with additional protein/fat. Instead of a lean skinless chicken breast, have a hamburger patty made with ground chuck - more calories, but you don't add carbs that way.