I am a currently an undergrad sophomore and am aiming to go to grad school for a PhD. I would like to do research with a professor at my school during the semester for (among many other things) graduate admissions. However, I have been able to secure a mentor or arrange for this research over the past ~year. I have contacted many professors by email (and sent polite follow up emails after a few weeks) but only a couple responded, and they said they were too busy to work with undergrads. After that strategy yielded no success, I tried to go to professors office hours and talk to them face-to-face; however, the majority said they were too busy, were already at capacity with undergrads, or did not have a lab/research area that was well-suited to undergraduate research.
The professors' reasons are of course completely valid, but I am very worried about finding a research opportunity and the attendant impact on grad school admissions. I have spoken with more than half of my school's faculty in my major (and many of the remaining faculty do not have significant lab groups and only work with one or two graduate students at a time). I believe that part of the problem is my school—it is very highly ranked in this field in the US, and the undergraduate population is very competitive. I am a slightly above-average student in the department, but I can't compete with the very top group for research positions. Would it be advantageous to transfer to another university with a lower-ranked department in order to increase my chance of finding a research position? Or should I just contact the professors again next year? I have also considered expanding my search to other departments, but I am less interested in those areas and unlikely to pursue them later.