Not exactly helping answer your question, but I'll share my experience as another data point for w/e it's worth:
The biggest two questions I can ask you are: how important is it to you to get into an REU this year, and how annoying do you find the application process?
I hated the application process (all application processes, really) and thought an REU would be neat but wasn't sure I had the credentials.
I applied to 4 and got into one after two years of college. In hindsight, I was surprised I got in having had minimal experience in what courses I could have had under my belt at that point to help me make sense of the research they had me doing. Perhaps I just got lucky, but never the less, I went to the one that I was accepted to. My dad advised me to apply to at least 8, but honestly, If I got rejected from 7 and only got into 1, I probably wouldn't have felt very confident going to the 1 that accepted me, and thus might not have gone.
All that being said, I don't regret going at all. I got a rare opportunity to perform interesting research (whether it really made a difference is altogether a different story), networked a bit, and had fun with my roommates on down time.