I am not Celiac in the true sense (no intestinal villi damage), but I have awful gluten intolerance and tested positive for gluten antibodies on a stool test (gross, I know). On top of this, I am severely reactive hypoglycemic (which my doctor thinks might be due to consuming wheat). I have been trying to eat fewer grains and more veggies for fiber. Ironically when I'm eating grains, I get diarrhea and when I eat only meat (mostly fish & chicken), veggies, fruit, and nuts, I am "regular." I'm sure you don't want to hear about my poop, but I'm just pointing out that sometimes, we really don't need grains to function well. Wheat and oats give me TERRIBLE acid reflux. So does corn, soy, and legumes like beans and peanuts. I don't know what is wrong with me, but the only things I can safely eat without any reflux or other gastrointestinal distress are cottage cheese, whey protein shakes, fish, chicken, some fruits, and all vegetables. Nuts sometimes give me heartburn and sometimes don't, but peanuts (which are actually legumes) give me horrendous heartburn.
Are you able to eat quinoa? I'm not sure if you can eat that. It doesn't have as much fiber as whole wheat pasta or anything, but it's really delicious and I believe gluten-free. When I'm in the mood for some sort of grains, I eat brown rice or quinoa. My stomach is just so sensitive to any grains at times. It's like I secrete extra HCl (acid) in my stomach that requires me to eat protein so it has something to digest. So, I try not to eat hardly any grains.
I wish I could help you out more! But I don't really know what to say.
Oh, yeah, what about fruit & veggies for your fiber instead of grains? Apples & pears especially have a lot of fiber. So do berries (esp. raspberrries). My favorite breakfast is a whey protein shake (I use Jay Robb's strawberry whey) with either frozen raspberries, strawberries, or blueberries (or all three if I'm feeling adventurous!) and a tablespoon or two of almond butter mixed in. That shake usually has 7 or more grams of fiber from the almond butter & berries alone. Or, if you eat an apple with almond butter, it can be up to 10 grams of fiber depending on the size of the apple & amount of almond butter (oh, yeah, I'm sure PB is fine too...it just makes my reflux really bad, so I don't eat it). Legumes are full of fiber if you can digest them. Spinach is really full of fiber (I think there's 6 g. in one cup of leaves).
There's lots of simple things to increase our fiber intake...grains aren't the only way. And for many celiacs with intestinal damage, grains (in any form) can make things worse. I'm not sure if that's you, but I know a couple celiacs who have to abstain from all grains to feel their best.
Anyway, I hope some of this rambling helps!