I think if you want math, you should consider majoring just in math. If you want engineering, then don’t apply for Williams. This will impact what you do in life - it’s not just about - school name.
And if you like Boston, will you like being in the middle of nowhere (Williams)?
I mentioned Bama solely because your 4.0 and 36 get you free tuition, a year housing, $1500 a year scholarship and $2K one time. It’s likely better than you’ll get at UK - and WKU just won’t have the academic heft for you that even UK will. Plus, UK is more urban and that seems like something you might like (even more urban than Bama). As for Bama, they have, if not the most, top 3 National Merit Scholars in the country, so no shortage of smart people. And it has aero.
I wonder - maybe incorrectly - if a school might turn someone down because they walk in with so many credits - like a private - as is you wouldn’t be there 4 years.
If you like Boston, you can also look at Tufts, Northeastern and a bit further away, WPI. But again, a BU is $100K a year or close - so make sure you have that discussion with your folks. They can run the BU Net Price Calculator - I put below. Note, they are need aware, so if you needed, say a full ride or close to it, they could turn you down just for that.
If you like Boston because it’s urban, then Pitt and UMN would make great engineering schools in an urban environment. If you like urban, Penn might be a better school for you than Williams or Swat - then you’d have math and engineering.
As for Mac not having engineering, don’t put the blame on your counselor. You are a very bright individual - you can look up majors offered by colleges on your own. But you can continue to run ideas by people here.
Good luck