22 Open or short in engine coolant temp sensor system.
Bad sensor or wiring. If this code triggered the ECM will go into fail-safe mode and assume the coolant temp is 176F.
31 Open or short in MAP sensor system.
Map sensor or wiring. If this code the ECM keeps the fuel injection and timing constant to allow a get home mode.
71 EGR system malfunction.
Open in EGR circuit, short in EGR VSV, EGR hose disconnected, clogged EGR gas passage, ECM. If this code the EGR is shut off. Note: The EGR is normally off at engine idle.
Given the nature of the codes and the fact that a new MAP sensor resulted in no improvement the issue may be in the wiring.