I'd try a realtor's website, like
Long&Foster. There you'll find more private rentals. I know you said you don't want managed, but if nothing else you can look at
Yarmouth. They manage a bunch of places in Capitol Hill.
I tend to think of Logan Circle as more Dupont, but that's mostly because when I go there we usually end up walking to U Street or Dupont. Atmosphere-wise, it's a little quieter, so perhaps more like Capitol Hill.