It is not easy to transfer because there is typically very limited availability in high demand programs, like engineering or CS which require large resources compared to liberal arts. Engineering core courses also need to be taken and can be difficult to catch up on when transferring, and might require an additional year of school.
To answer the OP’s question, I would apply directly to engineering. GPA and rigor are usually more heavily weighted, and a high SAT II math score will offset the SAT math of 730. A bachelor’s in biology will have limited job prospects compared to engineering should the OP change his/her mind about med school (and still has to go through med school admission and residency hurdles)