Not wanting to quibble here, but most beans are NOT legal on the Specific Carbohydrate Diet. Kidney and black beans (and a couple others) are allowed "only when symptom free," and must be soaked and prepared as the book states so as to remove the excess starch.
Except for the "Intro diet" phase, I would not consider the diet low in fiber since most fruits and veggies are allowed. Also, almond flour is used in baking and cooking and is naturally high in fiber. My family loves a simple meal of pan fried fish (tilapia, orange roughy, fresh-water fish), breaded with almond flour and cooked in a little butter and oil. Lastly, it would be simple to follow the diet without beef as there are many fish, chicken, turkey, pork and lamb recipes.
The important thing, which goes to your initial question, is that this diet is gluten free--you can count on that! (Not pushing the diet here, just offering gluten free recipe options!) Also, there are many recipe books based on the SCD which also meet your gluten free request. I recently purchased "Recipes for the Specific Carbohydrate Diet" by Raman Prasad, and it was worth every penny!
I know there are others here who have had great success with a gluten-free diet. Yogaprof comes to mind...she'll be along soon, I'm sure!