I did it for years. I needed a Pulmonary Function Test and a letter from my treating physician, and if it is under control you can fly with a special. Your AME can tell you what you need.
You need a real AME, not a guy who does it as a hobby. He will know what needs to be done, what paperwork to send, and will know someone at OKC that can move things along. And the delay is only on the initial special, once it is in the system, you will get a medical at your physical afterward and they renew the special a few months afterward if nothing wrong.