I read nuclear, I think UTK.
I hear aero I think UTK.
I hear I have $75k but would like to spend less -I think UTK and a few others.
Given your stats, Alabama as well where you’d get $30.5k off $33k tuition or UAH, smaller and heavily aero focused.
Bama gets more smart kids because of this - loaded with national merit scholars but just really qualified kids (non natl merit) get $28k plus $2.5 for engineering vs other schools that charge extra for engineering).
Good solid schools will help you in all these mediums and UDel and UMN would be two great names for all majors but notably ChemE.
So given your budget UVA and UM need to come off.
You can spend $60-75k or more. UVA is $86k first year and goes up from there. Michigan is $76k the first two years and $80k after. It will be more later. Not sure engineerimg has a charge above like many do - Purdue, UVA UMN, etc
Your folks are right to consider fit. If you have ABET for most disciplines you are fine. My kid ended up at Bama over Purdue so he could get his own room. Bonus that he saved me $ but not why he went. He’s a manufacturing engineer at an aero firm.
Interned with ga tech kids in automotive - he got invited back, they didn’t. Works with kids from UM, Purdue, NC State, Ohio State but also Utah, Akron, W Michigan. The common thread - ABET.
If you want to spend more, then go see where fits. Va Tech is gorgeous and has top rated food. NCStates campus is a 20 min walk or short bus from the main. UTK has a great rep today from OOS but of course in state kids like mine dismiss. . Rice is smaller but has the Rice investment if you qualify - look it up if your folks make under $200k. (go TO there - but it will be an impossible get unless you can bring up your non stem ACT).if you like that size there are other options for you within budget.
Go check them out - but bang for the buck - saving your folks $200+ vs budget you have UTK, Bama, UAH, MS State - all good.
But if nuclear is likely, your best bet is to stay home.
Of course lots of schools can get you to price with a $75k budget. . Those on your list and more.
For chance me, I’d say UVA, TX, Michigan and Rice would be a reach.
Purdue high match / low reach. .
Va Tech, NC State low target…
Have you considered UF, like Purdue it’s value priced OOS. I also know kids at UK who’ve done well (I’m in Williamson County TN). No one talks UGA engineering but your high STEM ACT can help get u money if you raise the reading. It’s solid.
One last to look at - Arizona - wonderful in aero. Doesn’t have nuclear but with 17 majors likely one close enough. You’d get $32k off tuition so not Bama cheap but $25k a year all in.
These schools will all get you go the same place so if saving for your folks (maybe to help with your first home) is important - well you can hold to your list or save them a boatload.
Best of luck.