In continuation of our systematic effort to understand hadronic matter at high density, we study dense skyrmion matter and its chiral phase structure in an effective field theory implemented with the trace anomaly of QCD applicable in the large Nc limit. By incorporating a dilaton field χ associated with broken conformal symmetry of QCD into the simplest form of skyrmion Lagrangian, we simulate the effect of 'sliding vacua' influenced by the presence of matter and obtain what could correspond to the ``intrinsic dependence' on the background of the system, i.e., matter density or temperature, that results when a generic chiral effective field theory of strong interactions is matched to QCD at a matching scale near the chiral scale Λχ∼4πfπ∼1 GeV. The properties of the Goldstone pions and the dilaton scalar near the chiral phase transition are studied by looking at the pertinent excitations of given quantum numbers on top of a skyrmion matter and their behavior in the vicinity of the phase transition from Goldstone mode to Wigner mode characterized by the changeover from the FCC crystal to the half-skyrmion CC crystal. We recover from the model certain features that are connected to Brown-Rho scaling and that suggest how to give a precise meaning to the latter in the framework of an effective field theory that is matched to QCD .