With what style should I write to a Board Of Examiners?
There are a number of comments on here regarding your use of intensifiers in the example sentences. Overall, I would avoid these because, while this is an emotional issue for you, it is unlikely to be for the Board of Examiners. It is important to present a "face" that is perceived as rational and objective, not overly emotional or making excuses. I have personally found that becoming emotional while trying to assert my needs has generally ended up undermining my goal (whether or not this SHOULD be the case is another issue entirely, particularly in the case of physical or mental illness when one has not as many resources to advocate for oneself). 

That said, wherever possible, try to replace "empty" sentences with examples. For instance, instead of "this process took very long," quantify how long it took. Instead of "despite my best attempts," describe in detail these attempts. Instead of "I really attempted to avoid," describe the measures that you took to avoid [whatever thing]. Perhaps this is the scientist in me talking, but I always feel factual details are the most convincing.