Here’s a list of colleges that claim to meet 100% of demonstrated financial need:
https://www.usnews.com/education/best-colleges/paying-for-college/articles/2016-09-19/colleges-that-claim-to-meet-full-financial-need
For the “full need” claim to be true and meaningful, I believe it must pertain to all enrolled students, whether domestic or international, and however they apply (ED/EA/RD). That’s not to say that financial need, nationality, or the application round doesn’t sometimes affect the admission decision. Very few schools are both need-blind and claim to meet full need for international students.
Merit scholarship applications typically have early deadlines anyway, and some of the biggest scholarships are awarded automatically for qualifying stats. So in those cases, the ED/RD distinction may not matter much.
http://automaticfulltuition.yolasite.com/
Especially if you’re considering schools that neither claim to meet full need, nor grant large merit scholarships automatically for qualifying stats, then it may not be to your advantage to apply in the ED round (since, if accepted, you won’t be able to compare offers). In any case, being an international applicant is a disadvantage in seeking FA from most colleges.