I think it will take some time to get the answer we are looking for, we'll need to get in touch with the engineers. In my mind - this working depends on whether the NVR uses Passive POE or Phantom POE. If it's passive POE - that uses your unused pairs. If they use Phantom POE then your plan might work. We just need to know how the POE works on the NVR.
I may be totally off the mark here, but that's my 2 cents worth.