I'm not familiar with what settings the D7000 has available, but if you've got "noise reduction", I'd try that for the graininess.
I know people slam noise reduction as something the purists will never use, but these are also the same folks that drop the sharpness down so sharp edges are all softened for the sake of a more natural PQ. Well, when I look at the world around me I don't see grain, so why not use NR if it's available?
My example was watching "Pawn Stars" and noticing that the black shirts those guys all wear were a little noisy with NR off, so I turned it on & it got rid of 90% of the grain. (nice). Sure it softens everything else just a tiny amount too, but I think the fix is worth it.