Hi Peter - I am puzzled - Exif tool (hosted in mac GraphicConverter) says no profile for the 1st one & opRGB for the 2nd and very little exif info on either (1024x768 files)
The one thing that is essential is that to be "sRGB" as the world/web knows it, it has to be the genuine article sRGB IEC 61966-2.1
As I said above, the sRGB in camera setting on the D7000 is Nikon sRGB which is different from the IEC version in Capture NX2 and it is only that and View NX2 that take any notice of what is set in camera as far as I can tell. Have you tried doing 1st stage conversion using View NX2, but not altering anything? I am not familiar with GIMP.
My own conclusion has been to keep to my D80 practice of setting camera to Adobe RGB and converting to IEC RGB immediately before saving a jpg for the web