In this work, we designed microcavities with varying detuning, defined as the energy difference between the microcavity mode at normal incidence and the exciton absorption. This approach allowed us to shift the energy of the lower polariton and control its overlap with the emission maxima of the exciton reservoir while tracking the energy dispersion of the photoluminescence (PL) from the lower polariton branch. This provides us insights into the efficiency with which the exciton reservoir radiatively feeds the lower polariton. By performing this experiment as a function of temperature, we identify that the population distribution of the lower polariton depends on the spectral structure of the exciton reservoir emission. Similarly, we observe that the efficiency of radiative pumping at different energies in this system depends on the non-resonant pumping fluence, which impacts the spectral shape of the emission of the exciton reservoir. Finally, we conclude that the multiple radiative pathways from the exciton reservoir decrease the effectiveness of radiative pumping in these systems at low temperatures, by allowing radiative recombination of the exciton reservoir at energies that do not directly populate the polariton ground state. This presents a major barrier to achieving polariton condensation.