The calibrated profile will no doubt improve things, although it tends to be specific to images shot under the same type of lighting as the calibration target. Adobe calibrate to a mix of lighting conditions (which in my view doesn't do a great job with any but that's my unashamed personal bias!). NX2 or Capture One would no doubt do a better job of the colour rendering.
The XRite ColorChecker Passport I do use and it works well. However, I don't think that this will help you as you need to use it or include it in an image at the time of shooting and so doesn't help much after the fact.
I'm intrigued by your Capture NX2 problems - what Mac & version of OS X & NX2 were you using?