You would be eligible for significant merit aid at Miami University of Ohio, which has a good engineering program.
So, in theory you can afford to pay full freight at UVa and W&M (~$45K/pa) but not Cornell (~$56K/pa).
If a Catholic school is OK, a number of Jesuit Colleges on the east coast are the mid-size college you like and may give you good merit aid (ex. Fordham, Fairfield, Loyola MD etc.) http://www.ajcunet.edu/institutions
OP, FAFSA doesn’t give you money. It is a form to see if you are eligible for a Pell Grant and to be able to take out a a Stafford Loan. If you can pay 45 K a year you won’t be eligible for any Pell Grant money.
Ask for a budget range that your parents can afford from income and savings. “we can figure it out” rarely if ever works.
Check out University of Dayton’s engineering program.
All great choices with another one being Drexel. With your grades they’ll likely roll out the red carpet whereas you’re highly qualified for some of the others, but the global and geographic-diversity competition are fierce.
Your safety schools in state for your major are UMBC and UMD-CP. Both have sticker prices well under the $45k you say your parents will pay even before you get any merit money from them. You will likely get some scholarships from both of these schools to defray the costs even further. Get those applications out early and you have your safety schools.
It’s going to be very difficult to compete with the possibilities with those two instate schools in terms of price. UMD-CP is an excellent school with a great engineering program. Trying to get a full tuition or more award from the likes of Pitt, UDel, UNM, UAlabama etc is certainly possible but it’s not like you are getting so much more luster for the money, which is what you want. Other posters have come up with other options. Check them out
You are already applying to University of Delaware and they are very generous with merit if your test scores are high. We are OOS and UD ended up being one of the cheapest engineering schools for our daughter. Their honors program is also very highly regarded. If you want to go farther away, check out Iowa State. Excellent engineering school with rolling admission and very good merit.
UMD is not a slam dunk for Chem E, though you should have a very good shot – scroll to Incoming Freshman Class Profile eng.umd.edu/facts-and-figures
I think UDel is a very solid choice, esp since the state is so well known for its chem industry.
We know a student who went to St. Mary’s MD in Chem and went on to a Big Name PhD program.