I can feel your frustration, they say they haven't got your letter, typical.
I dont know anything about appeals so i'm not much use, but I feel for you and what you must be going through.
They should have specialists not gp's !?! dont understand why they dont have specialists.
all the best, let us know how you get on, do send another letter by recorded delivery. I bet you've had enough of appeals and letter writing, but keep at it. They should also be looking at what you cant do and how this effects your life, its disabilitating!!
good luck hun