"Do I assume the local wages are the actual NY wages and override in the PY/NR screen?"

No. What you seem to want is that the three States should = Fed, but that's not how it works. Each State has their specific way to handle this. Some will have you report all wages and they credit back the tax paid to another State. Some will have you report only what is for that State to tax. Some tax on Source employer/location worked and some tax on Residency.

Enter the data as it was presented to you, per State as named.