Are you sure it isn't the wheat in baked goods you are reacting to? Have you ever been tested for gluten sensitivity? Antigliadin antibodies? If you haven't been, I would ask your doctor for this test. In fact, the entire celiac panel should be run.
Yeast can also be a factor for some people, contributing to neurological symptoms, so you could be on to something there.
You might also want to keep a food journal and experiment in a systematic way. Others here have more experience with an elimination diet, but it might be worth doing to see if you notice any significant improvements.
Celiac Disease provides us with such a good model of how food sensitivity can cause neurological disease through both immunological and nutritional factors. I think it is worth at least considering whether it might have any influence at all in other neurological disease, or if it might co-exist with another condition that already exists..worsening symptoms.
Have you looked into any "alternative" treatments for PD? I don't really know anything in any depth about PD, but here are a couple of "alternative/ complementary medicine" sites you could look through. I've found the Nutritional Healing site seems to do a good job of pulling together all that is available on the net in regard to alternative treatment for many conditions, including book recommendations. They have an entry for Parkinson's Disease.
P.S. I just stumbled upon this on another forum...someone who was originally dx'd with PD, and later with CD. You can enter the forum as guest just to read: