You need a budget - full pay can be $90k or $400k.
What type of engineering ? That will impact.
You’ve heard many - UCONN, Quinnipiac, Delaware, URI, Maine, RIT, Drexel, Cincinnati, WVU, Syracuse, Hartford, Pitt, Akron, SUNY Buff, Miami Ohio and more,
Since WUSTL in play, how about Mizzou, Iowa, Iowa State, Minnesota, Michigan State.
I don’t see UVA or WUSTL as viable but you can try.
I think what type of engineering can help direct the student and frankly in most cases, no need to overspend. Outcomes don’t necessarily deviate much.