I noted this of UMD and Pitt - not impossible but not likely.
The alternatives area wise that would likely be affordable are Delaware and would be affordable is WVU. If the student wanted an urban school like Pitt, it’s larger but UMN should work with merit. UT Chattanooga on a smaller city level.
While I can’t imagine Va Tech not being likely, I know this year’s thread showed really tough #s for in state.
Bottom line, if the budget limit is $50K, then OP needs to re-arrange.
Given that # was given for privates that are super reaches, if the student didn’t want to dial down that private list, they’d have to add some such as RPI (maybe), RHIT (maybe), Clarkson (highly likely) and others - to hit budget. My maybe/highly likely refer to $50K. All would be admissions.
Yesterday someone published an article about Syracuse - they weren’t giving money but at the very very end, if you waited, they came out with crazy merit - so that could be a long path possibility for one willing not to commit to somewhere - to see what happens.