The short answer is -- Yes, you can protest. In my experience, there are national firms who do this, and Judges know it. But you should do it as soon as possible, and include all the facts in your letter.
Contingent usually means the attorney gets paid if you win. The per centage is usually of back benefits,but you need to read the document to see why there is a range of 30-40%. Most SS attorneys only charge 25% of back benefits. Consultations are usually free so talk to more than one before deciding.