I've been eating grain free for several months not due to celiac, but because I experimented with it and found I felt better. But I've also cut out most sugar. Most GF foods use substitute 'flours' that are high in gylcemic load and low on nutrition, so I no longer eat those. I do NOT watch calories or fat, but choose healthy fats. A couple of great resources are
http://www.wheatbellyblog.com/ and
http://marianutrition.com/ . I mostly follow their guidelines, and they have lots of good recipes too.
Only downside to eating this way is that I've lost weight, none of my pants fit anymore, and I have a hard time finding new ones as they're all WAY too big in the waist!! LOL