Vibrational sum-frequency generation (vSFG) offers interface-specific spectroscopy under ambient conditions, yet extending it from extended optically flat samples to nanoparticle (NP) ensembles on dielectric supports is hindered by scattering, phase ambiguity, and film inhomogeneity. z-cut α-quartz is widely used in vSFG as a convenient standard for both intensity and phase reference. Building on recent work that deposits NPs on z-cut α-quartz and employs an internal normalization scheme, we introduce an eight-degree-of-freedom stage that preserves the same micrometer-scale spot during azimuthal rotation. This capability enables phase-contrast measurement across complementary polarization families without changing the probed area. Applied to Mn-doped Co3O4 supported on quartz, the workflow robustly recovers the imaginary spectrum, Im{χ(2)}, of surface-hydroxyl vibrations with internal normalization under different polarization combinations polarization sets. These advances deliver a practical, internally referenced, and phase-resolved vSFG protocol for NP ensembles on dielectric supports, extending operando access to catalytic interfaces beyond metallic or plasmonic enhanced architectures.