> But should you learn integration before differentiation? I’d never considered this approach until I read David M. Bressoud’s fantastic book Calculus Reordered,

Ha, I learned calculus integration first from Ivan Niven's "CALCULUS An Introductory Approach," copyright 1961, that as a kid I found in the attic in my dads undergrad engineering books. When I got to high school and took calc, I was able to do all the stuff they were teaching, but in weird orders and methods compared to more modern books.

Now, 40+ years later, I still have that book on my bookshelf in the calculus section :)

Till now, it's it only book I've seen that teaches it this way.