The other concern is that starting outside of engineering, the student may potentially take longer to graduate, even with APs due to course sequencing. My son started as a 2nd year but still took four years due to this.
The research provided by UND before by @vpa2019 is the type OP will need to do for each school. Engineering is a different ball of wax then other departments.
OP plans to start at Carroll School of Management but has Clemson Engineering as an option but deciding not to attend.
So that will be the challenge he faces and from a cost POV UMASS and UMASS Lowell are good suggestions.
Transfer scholarships will vary by school - but if you took an Alabama for example, as a first year, someone with a 3.5 and 32 ACT would qualify for $30,500 off the $32K tuition. But as a transfer, it appears the best case is an OOS waiver for two years and potentially another $3000. These can only happen with 45 credits. So that would be much less robust.
As the student is headed to BC, it’s likely OP is full pay - so cost elsewhere may not be a concern for this student.