I don't have much help to add on the "how" to go about this. But after doing my appeals, focus on personal letters from your doctors either adding new information that may not have been considered or letters reinforcing why you are appealing that your doctors agree with your position. the FPEB needs to be persuaded by professional opinions. Your personal opinion doesn't carry much weight with the FPEB - they want to make their decision based of facts from providers and professionals.
I never appealed to the FPEB on incorrect ratings, I appealed they were incorrect instating I should be found unfit. My letters included signed memos from my Squadron and Wing commanders on how I won SNCO of the Quarter while supposedly "unfit". A letter from a Brigadier General on the board for Air Operations Intelligence (I worked under him when he was our wing commander) on my work ethic. I had letters from doctors stating that my conditions didn't cause any unsafe working hazards to myself or co-workers nor was I unable to do the duties of a SNCOIC. I still was denied and the unfit finding stayed.
Not to discourage you after my denial, but I offer these words as an example of the level of communication you should be bringing to the FPEB. If you have any personal contacts in offices high up, I would be begging for a favor right now. At least have letters from every commander and/or Chief and First Sargent in your chain of command on base you can and any doctor that will write a favorable letter to you.