Well, I haven't heard of the disorder until now, but I did some googling and found some stuff.
First, just so you know, not all naturopaths insist on a meat-based diet. The two I've seen are totally accepting of me as a vegetarian. You might want to call around and talk to some others about your case, and ask if they are willing to treat you while you maintain your vegetarianism.
Second, it rings alarm bells in my head that this ND just diagnosed you with this very difficult-to-diagnose disorder that she also has. That would make me suspicious, personally. I think some doctors are all too eager to diagnose you with whatever they are familiar with and feel they can treat. So I would get a second opinion for that reason, too.
From the few pages I saw that discussed it, it didn't seem like you would need to eat meat to stick to the diet--just to avoid irritating and high-fiber foods for a period of a few weeks. Low-fiber diets are very bad for most people in the long term, however.