The NAD you noted has Dirac built in I believe. Room correction software is a different animal but can make a great difference when use properly. If you aren't techy Dirac can be somewhat difficult to navigate. In that case I'd suggest finding a local dealer and have them do it.
The MiniDSP is a cool piece but in your set up using a integrated you'd only be able to use their product on the sub channels whereas Dirac can do the full range including your subwoofer(s).
Just something else to think about.