[en] Phase-of-the-phase (PoP) spectroscopy is extended to two-color laser fields having a circularly counter-rotating polarization. In particular, the higher harmonics of the (two-color) phase information are analyzed in order to extract the laser-coherent part of the photoelectron spectra taken under complex target conditions. We illustrate this with a proof-of-principle simulation by considering strong-field electron emission from argon atoms within helium nanodroplets under realistic experimental conditions, i.e. a limited number of photoemission events. Multiple elastic scattering on neutral helium atoms creates a laser-incoherent background, but the higher harmonics of the PoP-signal allow to resolve the coherent contribution to the photoemission. (paper)