It seems to me that there's more than one idea that needs to be addressed.... I see:
* Cheating (one test; small problem);
* Perfectionism (larger problem that seems to be driving the cheating);
* Blaming yourself for things beyond your control (parent's disease; a common condition felt by responsible parents);
* Thinking something is worse than it is because you're wound up and can't see the forest for the trees (cheating on a spelling test when he felt scared makes your son human, not a pscyhopath
).
I agree. Also, if the school already gave him a punishment, as they should have, I don't know if I'd have made him write apology letters, although I'm not suggesting you're doing something wrong either. In my opinion forcing him to write the letters may do little from his point of view except to further humiliate him. I also don't think he should have to apologize for the disappointment of others; it seems like double punishment to me.
What he did was break the rules, which I guess constitute a social contract with others not to cheat, but if he is already punished for cheating then breaking the contract is covered. I'd focus on conversations with him about why rules against cheating exist, how winning by cheating isn't really winning and doesn't make us feel good in the end, how disappointed others must feel, etc.
