I don’t have things like letters between Egyptian military leaders, large treatises, etc., like I do from the American revolution.

It doesn't matter what you have. What you have is the things they chose to publish.

Put it this way. If the rebels had lost the war and the British had won, do you think that the British history books would give the same reasons for the attempted rebellion?

If those are the actual reasons, there's not going to be any case of "history is written by the winners". Boy would the British history books look grim, they crushed an attempted rebellion where the rebels had such lofty ideals!

Or, do you think the alt-history British would look deeper and say something like "While George Washington publicly claimed to be rebelling because he objected to the lack of representation, in reality he had purchased a lot of land illegally and was trying to justify the revolution so that he could make a profit on that investment."

You seem to be hung up on this idea that people who write about their justification for rebellions and coups are being honest, for some reason. They aren't. The public reasons they give are the ones that make them look good. You need leaked recordings or investigations to uncover the reasons that they don't list in public.

In this case, historians have dug into the actual reasons for the rebellion. Sure, to some extent the rebels may have felt these lofty ideals, but they were also trying to get rich. They wanted access to all the wealth of the American continent without having to share it with the people of mainland Britain.