The one that jumped out at me on this list was Kettering, as it’s small but still has great ties to the auto industry, it’s attainable admissions-wise, and it has MechE, Management, and Industrial Engineering, which has both business and engineering components and might be a really nice, flexible major for your interests. They also emphasize co-op education, which might appeal. It may be more urban than you want, though.
TBH I’m not getting a clear sense of what appeals to you academically. The fact that you enjoy working on cars, and perhaps are very good at it, doesn’t necessarily mean you’ll like studying engineering. Do you have a particular interest in the auto industry, even outside of hands-on work with cars, or not necessarily?
What language have you studied, and are you interested in studying abroad? Several schools that have dual-degree programs in foreign language and engineering/business, get students into great auto-industry internships and careers in their target countries. (Especially in Germany and Japan, although I realize it’s unlikely that either of these was the language you studied in high school.) U of Rhode Island (smaller flagship in a lovely coastal location, not urban - has some good SCUBA opportunities too) has both International Engineering and International Business. (And again, Industrial Engineering is an option within International Engineering - this major could give you a lot of flexibility to fine-tune what you want to do across engineering and business, as you gain experience.) Would something like that interest you? (URI has a top-notch Ocean Engineering major too, if that’s of any interest.)
Speaking of ocean-oriented stuff, is your mechanical bent specific only to cars, or might it extend to boats also? A student with strong hands-on mechanical aptitude could have a great experience at one of the Maritime Academies. (Participation in the Corps is optional at many, and there’s no service obligation.) For example, Maine Maritime has multiple options for engineering, engineering tech, and business, and tons of hands-on experience, summer training cruises, etc. Same with Cal Maritime, which has just become part of Cal Poly SLO and would be a way in to a SLO degree. (The main SLO campus wouldn’t be attainable with your stats, but the Maritime campus could.)
Speaking of Maine, the UMaine flagship can be a great bargain for OOS students because of their flagship match program, and their strong engineering school has both MechE and MechE Tech (the tech major could be a good option in case you find MechE too theoretical and not hands-on enough for your interests)… plus all of the usual non-engineering majors are available - business, psych, etc. Only about 9K undergrads at UMaine.
But maybe you can give some feedback on your interests, and whether you’re especially seeking a career in the automotive industry, or whether you just like hands-on mechanical things generally… and how your interest in psych figures in. If you’re thinking of psych in terms of the “human factors” aspect of engineering, some Industrial Engineering programs have this specialization.
In that vein, maybe Michigan Tech would be worth a look. Smaller (under 6K undergrads), rural (Upper Peninsula), and their Psychology & Human Factors major could be a great crossover between your psych and technical interests. They also have a traditional psych major, and a full range of engineering and business majors, including MechE, MechE Technology, and an Entrepreneurship concentration within the Management major. Michigan Tech is a little reachy for your stats, but not unreasonably so, and they have a “test flexible” option where you can submit AP scores in lieu of SAT/ACT, which might be more advantageous for you than going fully test-optional (although they do have a TO option also).
P.S. If you like the Human Factors idea, there are a few other undergrad programs in this area (although the majority of programs in this specialty are grad programs). Again querying whether your mechanical interests flex, this time toward aerospace… Embry-Riddle has this too, both in FL and in AZ: Bachelor's Degree in Human Factors Psychology
Overall, I agree with ColdWombat’s encouragement to seek out schools that have multiple majors of interest and that don’t make it difficult to explore/change major pathways.
