Big school to solid and strong LAC? (Chance me Please!)

Hi I am an freshman at one of big public school and my major is civil engineering. My school is pretty well known in the field and the location is nice, but I feel like it is too pre-professional and does not fit my personality.
I prefer small classes with lots of interaction between professors and students but at my school there are about 400 kids in every class I am taking, and even if I go to the office hours, (which I go pretty often) there are like 20 kids everytime so it is really hard for me to get close to the professors. I am thinking of transferring to small but good liberal arts school with solid science program. The school does not have to offer engineering major but good math, physics, or other good pure science program is great to me.
I was thinking about schools like Harvey Mudd/Weslyan/Olin/Scripps/Vandy/Rose Hulman/Hamilton/Colgate/Vassar/Pomona/Swarthmore/Cooper Union/Rice (it is not LACs but it is small)… and many other really good LACs that I can’t think of right now. My top choices are Rice, Swarthmore, and Mudd but I think they don’t accept
Do you think it is worth trying or does this sound totally absurd to you??
Can you recommend me some schools that I have chance getting in or chance me for the schools that I mentioned above? I am an international student.

My SAT is not really high 2160 (CR 620/ M 770/ W 770) compare to that of the students of the schools I want to go. But I am not sure how important my SAT scores are in transfer admission.
I don’t know my HS GPA but I was all A student until Jr year and got 3 B+ (all APs) and 3 A&A- (for regular classes) in senior year. I took total of 6 ap classes and got 4s and 5s. I am only taking 4 classes this quarter (3 classes w/ grades and 1 p/np) and there will be one more quarter before the deadline so I would take total of 8-9 classes until March. I am aiming for 3.7~8 for gpa or higher and my midterm and quiz grades are pretty good so far but there are not many grades yet.
I have lots of ec but nothing special. (Drama/NHS/Tutoring experience/ Math competition …etc) and work as an intern at small company for three summers and now work as an intern at local high school offering math and science tutoring.
My last year’s essay was good and have another good story to write about.

Do you think it is worth trying? Thanks

Do you want to be a civil engineer after graduation? If so, then you want to transfer (or stay at) a school where you can study an ABET-accredited civil engineering major (or at least an ABET-accredited general engineering major with civil engineering options and in-major electives, as offered at some smaller schools).

You may also want to consider smaller engineering-focused schools. In your list, Rose Hulman, Rice, Cooper Union, and Vanderbilt have ABET-accredited civil engineering, while Harvey Mudd and Swarthmore have general engineering.

Other smaller schools you may want to consider include:

Colorado School of Mines
Illinois Institute of Technology
New Mexico Institute of Mining and Technology
Michigan Technological University
Missouri University of Science and Technology
South Dakota School of Mines and Technology
Stevens Institute of Technology
University of Alabama Huntsville
Worchester Polytechnic Institute

However, you need to check on such things as transfer likelihood, affordability, and transfer credit at each one.

Your college courses and grades will be highly important in determining your likelihood of transfer admission.

These colleges appear in a Princeton Review sampling, “Great Schools for Mathematics Majors,” and would be worth researching individually (schools do not offer direct engineering majors):

St. Lawrence
St. Olaf
Macalester
Reed
Grinnell
Carleton
Haverford
Hamilton

Though some, perhaps the majority, of these colleges could be high reaches for you, two or three nonetheless might be fully receptive to your application.

This too.

Mudd is very difficult to transfer into. They only take a few transfers a year. It is hard to catch up with the core there.

Olin doesn’t have a formal transfer policy. You would apply the same way any other prospective first year student would, and if accepted you would start as a freshman. Their program is pretty unique and no credits are accepted from other schools (with the exception of Wellesley, Brandeis and Babson).