Why private?
UAH is surrounded by industry as is Florida Tech - but they miss the progressive off campus - and likely on campus part. A lot of aero is in the south - although there’s some in Colorado (School of MInes, again public) has MechE with an Aero Minor - don’t know if the school is progressive but the area is - but it’s a public, etc.
Engineering seems to develop well with public schools.
WPI might be another to look at private school wise - I don’t know if the school is progressive but the area is. Illinois Tech might be another.
Good luck.