You could always go to a college with a NROTC unit, join the unit without a scholarship, and work your butt off to get a two or three year scholarship. This was definitely a possibility when I was going through the college app process, but I'm sure more recent NROTC guys will chime in about how it works now.
As far as the engineering degree, I hope you're doing it because you actually like engineering, instead of doing it because you think you'll get a pilot spot. Take it from a history major, you don't need to be an engineer to get into Naval Aviation. I know education, general science, and english majors that are all pilots. Good luck though, this site will definitely help you find any info you need. Try using the search function for more specific info on the NROTC 2-3yr scholarships.