Surprised nobody has mentioned Texas A&M for NMS/F and it’s a top 10-20 engineering school. For NM Finalists you get instate tuition and the scholarships are minimum $10,500/yr. you’ll get just about full tuition covered.
Univ AZ is excellent for NMF $38K/yr covering full tuition for OOS. ASU not so great only $15K yr for NMF so you’ll end up with $23K/yr tuition.
Tulsa is full ride plus about $5K/yr for travel/research. Not too bad. I think bama is similar.
These are all good, but your best engineering school with NMF scholarships is Texas A&M.