Being a low income international student is not a hook. All of these colleges are need aware for internationals, I think. And as stated above, most don’t have engineering.
I’m not sure ED helps you. ED acceptances are to lock their most desirable students into attending. An international student with high need probably doesn’t fit that description. Also, you are obligated to attend with an ED app (although you can back out for financial reason, but it is stressful to do that). You aren’t going to be able to compare financial aid offers with ED, too. I will say that they might get fewer applicants from Egypt than other countries.
Many students who study physics go to college in their home country, then come to funded PhD programs in the US. I think that is probably also true for engineering.