I have made some great progress making gluten free sourdough bread. I am also allergic to eggs, dairy, yeast, and I have had trouble with some of the common gluten free ingredients like chick pea flour and tapioca flour. I experimented for a few years and came up with some really workable techniques and recipes. So far, all my recipes are rice based but I am working on a recipe for someone that uses millet as a base. Please look at the free recipes on my blog so you can get an idea of how sourdough can work for people with multiple allergies.
Please email me if you have questions.