Re: phase demodulator
Most phase detectors require comparing the instantaneous phase received to some reference signal's phase. The reference signal can be generated in the receiver with some sort of narrowband pll circuit.
The problem you have in using an FM detector is....that the frequency of your signal is not changing. So converting the FM of your signal into "am" (assuming you mean some sort of tuned circuit), you will get a constant "AM" signal as the phase is changed.
In some limited data types, you could use a delay line discriminator to detect changes in phase.