Difficulty finding research mentor 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.
This suggestion is totally "off the wall" and "outside the box", but the underlying idea is that you broaden your perspective. I'm assuming a few things. First, you are at a top institution. Next, you are a top student - you are obviously dedicated. Next, you aren't alone and there are at least a few of you in the same circumstance. 

Consider forming your own "research group". Become its leader. Find a faculty member who will give you a problem to work on and maybe give you occasional ideas on your progress. The commitment of the faculty member can be minimal and your research discussions are mostly among group members. Find someone, maybe even a postdoc, who can give you some ideas about research process in your field. 

But if four of you approach a professor it is a different sort of thing than going alone. A junior professor might be an especially good "target". 

Try to have your group meet a couple of times a week to share ideas and what insights anyone has. 

Produce a group report at the end of some period of time, even if it only discusses directions, not successes. You can even discuss failures, since it was learning that was important and it is just as good to know what doesn't work as what does in many cases. Offer the report to some faculty member and ask for comment. 

This will have two benefits. One is that it should enable you to learn something about research process even if it comes with small progress. Knowing how to go about research is an important skill in many fields and it is good to get some practice at it. But having formed such a group is, itself, a big plus when it comes to talking about grad school application.