Hi Jake,
I think the problem is more to do with the metering on the D7000. I used to face the same problem as you are, and then when I started underexposing the image by 1 stop, they seemed to be fine. I am still shooting a Documentary with the camera, and in some places where my anticipation of exposure goes for a toss, the image atarts looking like refined video. Rather than the crisp HD Film-like quality.
Also, the lenses that you are using will make a lot of difference to the way your footage looks. Using prime lenses to get the film look seems like the best option for now.
Kunal