Multidimensional coherent spectroscopy measures the third-order polarization response of a system to reveal microscopic electronic and many-body phenomena. Applied to semiconductor nanostructures, it can distinguish homogeneous and inhomogeneous broadening due to disorder or strain gradients, resolve coupling between transitions, and optically access transitions that are either non-radiating or outside the bandwidth of the pulses. Two tools often exploited in this versatile technique are (i) the ability to control the polarization of the excitation and emission and thus the optical selection rules, and (ii) the ability to capture the complex spectrum. Here, the polarization of pulses emerging from a multidimensional optical nonlinear spectrometer (MONSTR) and the resulting four-wave mixing emission are controlled automatically using variable retarders, such that multiple spectra are recorded during a single phase-stabilized scan. This improves the acquisition time by ~3x compared to running separate polarization scans. Importantly, only one phase ambiguity exists in the complex spectra across all sets of polarization states measured. This single ambiguity is resolved by comparing the initial spectrally resolved transient absorption to the complex four-wave mixing spectrum for collinear polarization and then applying it to all spectra. Here, the method is applied to a quantum well embedded in a semiconductor microcavity with an adjustable cavity-exciton detuning. The complex 2DCS spectra we report constitute the first measurements of detuning- and polarization-dependent exciton-polariton lineshape across the strong coupling regime.