phase difference 2 signals.

I will let FvM answer your question but since I am still awake I will point to these issues:

your signal seems sort of bipolar ref cos/-sin rather than cos/sin with dc.

The idea of atan per every sample will give you cyclic results that do not mean much unless you then compare it directly with ref.

My view is that you need to average the result of demod to remove the 120 MHz tone leaving only dc value that translates to phase through atan im/re and you should therefore settle at a fixed phase value eventually.

by the way atan is not easy to compute in hardware and you may resort to Lookup table use.