Putting GND on POWER layer
Its really a matter of capacitance and what your tying that capacitance to.
Interplane capacitance beween signals and a power plane is usually in the pico farad  to femto farad range. So if adding a ~1pf capacitor from the signal to the power plane makes a difference then go ahead and fill the plane, usually pF only matter with high speed signals after ~30-50Mhz and when transmission line effects start to take over.