I was a self-referral to Orthopedic Surgery at Mayo-Rochester; the process took about four months. You might have better luck if you ask your doctor(s) to refer you to a different department. Almost any department will do in terms of being able to see doctors in other departments. For example, I have gotten internal referrals to Neurology, Sleep Medicine, Cardiology, Dermatology, and Endocrinology. Does your systemic disorder have a dermatological appointment, for example? If so, begin there.