One thing to watch out for on the carnivore diet would be the caramelisation or browning of the meat. Caramelisation can cause the same symptoms as starch. It is for me one of my worst triggers.
I find that frying and browning in oil, for example, seems to be worse than cooking over an open fire. And if you were to baste the meat with anything sweet prior to cooking, it could be a recipe for disaster.
Another possible problem would be if you had an intolerance of one of the proteins. If carnivore doesn't give you the results you're looking for, a period of fasting might provide a quick relief from symptoms.