Pedigree, name recognition, and prestige will not get you accepted to medical school.
And you are already at a very good school. Classes will get more demanding as you get further into the semester and into upper year classes.
One thing that I do not see mentioned here is budget. Medical school is expensive. Whether transferring will help your budget I do not know.
The SAT is intended for high school students. Retaking it as a university student is not going to help. However, 1500 is already excellent.
You want your essays to sound authentic as if they were written by a young student. It is possible that your esteemed expert might understand this however.
One daughter attended a small primarily undergraduate university in Canada – basically the Canadian equivalent of a liberal arts college. She found herself in small classes taught by full professors. She got to know her professors quite well. This led to research opportunities. This led to very good references from full professors who know her very well. The combination of good research experience plus strong references from people who know her well led to a good research job in the US, and then acceptance at a very good PhD program back here in the US. There is a case to be made for small schools.
I think that the worse case scenario is that you transfer and do not like wherever you end up. Getting accepted nowhere and staying where you are is really not that bad an outcome, and can still lead to your getting accepted to very good medical schools in the future.