Bryce:
You won't need a carnet along the route you propose (in the order you propose it) until you get to Egypt.
The carnet exists for the sole purpose of preventing someone from selling the bike in a country other than the country that it is registered in. So, you appear to be at cross purposes with yourself (not that I am being critical of you, just pointing out an error in your planning logic).
There are a lot of posts here on this board about carnets - the subject comes up often. You might want to do a search on the word 'carnet', just within the paperwork section, and read the information that has been accumulated over the years. If you find any missing info, you can then post a question.
Your nationality is not an issue so far as the carnet goes. The only issues germane to the carnet are the country of residence of the person obtaining it (sometimes, but not always an issue) and the country of registration of the motorcycle.
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