I have thought about appealing directly to the Graduate School, but I'm not sure that's a good idea. If the committee's decision is overturned, I would still have to work with some of the committee, including two of the three who voted for dismissal, on my dissertation. It's a small department, and there's only a handful of people that I could use to form a committee for the project that I wanted to do. I don't think it would be a good environment for having to work with these people after essentially accusing them of poor judgment and of violating procedure.
As for retaking the exam again, the department doesn't want to do that because they don't want to set the "precedent" of allowing that kind of thing in the future. I personally think that's a bunch of malarkey, as I can think of one example where the department has granted an exception to another student, hence violating "precedent," but I digress.