If you do manage to get an appointment, rather than discuss all of the issues of the last 3 years have you thought about maybe just concentrating on one thing at a time? I just wonder if a different approach might be worth a try since you don't seem to get anywhere asking him questions about all of the symptoms you have?
So, for example, today you have posted on here about your throat being swollen, and it certainly looks it in the picture. Why not just concentrate on the thyroid issue, stick to the facts, don't go over old ground about why he's dismissed you in the past as that will use up the entire appointment time. Instead start afresh today, tell him what you want from him, what you expect, and be firm. Ask him why your throat is like this, what the different explanations could be and how he plans to rule them out. Tell him you believe it is related to hypothyroidism, and that internationally your TSH reading would be considered hypo, and ask him to prove otherwise with testing and an alternative diagnosis.
What I'm trying to say is I don't think you should waste your energy or time chewing over the same ground that you've covered in letters and previous appointments necessarily, because you will end up getting upset, and the appointment will be used up on that. Ask him if he is so sure it isn't thyroid, to give you a scientific reason and resolution that will make it go away and return you to full health xxx