Outstanding stats. You are definitely a candidate for schools with great aid.
In order to craft a great strategy, you will need your parents cooperation in filling out the NPC’s and seeing if the self-help portion is within your family’s means. Without knowing that, you really can’t craft a great strategy.
Basically, the fundamental question is whether your need based financial aid will be enough, or whether you need merit also.
I think the suggestions of Rochester, Lehigh and Case for merit are good ones.
USC, Rice, UChicago, Brandies and Tulane also have merit scholarships of varying amounts.
I think you might consider University of Pittsburgh where you might be able to get full-tuition. It’s not as automatic as Alabama, but if you apply early, you are a great candidate. They have an honors college, etc.
A second fundamental question is whether you think you want science or engineering. Engineering is a professional degree and therefore has many more requirements and a deeper prerequisite graph than science degrees do. To be a scientist, you really need a PhD. There are a few schools (Rochester, Johns Hopkins, Rice, MIT, Stanford) where you don’t have to decide until you get there, but most schools have different admissions processes for engineering vs arts and science. Some colleges have great science, but zero engineering (Brandeis, Chicago are examples).
$8,000 is a quite low to expect to get a college of your caliber, but perhaps you can do it.
Finally, I know you want to leave your state, but your stats suggest that you will likely head to grad school after you finish undergrad. Most PhD programs are funded, so they will pay you tuition plus a stipend. If push comes to shove, please leave your in-state option on the table until you are sure that you have something better.