Higher for what ? For MechE, short of a few schools, the where matters little. Mine turned down Purdue with merit for Alabama. Well he interviewed with 19 companies by Xmas and had 5 offers. He interned with two top 5 school kids. He went back a 2nd summer. They weren’t invited back. In his work cohort he has Michigan, Purdue, Washington, and Cal Poly but also Akron, Buffalo, Utah, W Michigan and more
You need ABET accreditation. The name is less relevant.
If you are a NMSF, Tulsa will be free. An NMF, Alabama gives you five year tuition, 4 years housing and $4k per year (which would cover food). Tulsa has the highest concentration of merit scholars. Alabama amongst the most, if not most. My son’s first year roommate was from Scottsdale. Others have good offers too - UTD is one often mentioned
So is saving $200k or $300k or $400k worth it to you when the outcome will likely be similar ?
So focus on what you want in a school - Smith is all women and small. OSU is massive. Some schools have or near gender parity. Others are mostly male. Some are huge with big sports, others aren’t.
Sounds like Tufts should be removed, based on budget.
If you want reach schools, then go ahead as long as that you have an assured and affordable safety that you want to attend (that doesn’t sound like ASU).
Tell us what you want in a school…you will be somewhere four years, day after day - going to a harder admit just because it’s a harder admit is sort of silly.