hi!
I applied to as many REU/research positions as possible last summer (summer before my senior year), because I really wanted to get experience at another institution before grad school. However, I didn't get in anywhere (even though I had decent prior research experience)...it seems like that process is more competitive than the actually phd application process, just because there are very few programs and tons of applicants (and I am definitely having more luck with the phd programs than I did with the summer research stuff!).
So definitely go for it, but know that you can still make everything work out even if you don't get a summer position! And also, if you aren't accepted anywhere, I recommend emailing a professor from a nearby university whose research interests match yours and volunteering to be a RA for them this summer (for probably at least 10hrs/week). I did that and it really strengthened my applications-- not only did I get to work with an amazing professor, but she wrote me a rec letter and I was invited to interview for the phd program at her university!
Just for reference--- I applied to University of Maryland, Oklahoma State, this APA summer program, and NIH/NIMH.