InP/ZnSe/ZnS quantum dots (QDs) offer a cadmium-free solution to make white LEDs with a narrow blue, green and red emission peak. Such LEDs are required for display and lighting applications with high color gamut. An important phenomenon that hampers the efficiency of such quantum-dot-on-chip LEDs is re-absorption of already converted light by the QDs. Proposed solutions to remedy this effect often rely on complex or cost-ineffective manufacturing methods. In this work, four different RGB QD-on-chip LED package configurations are investigated that can be fabricated with a simple cavity encapsulation method. Using accurate optical simulations, the impact of QD re-absorption on the overall luminous efficacy of the light source is analyzed for these four configurations as a function of the photo-luminescent quantum yield (PLQY) of the QDs. The simulation results are validated by implementing these configurations in QD-on-chip LEDs using a single set of red and green emitting InP/ZnSe/ZnS QDs. In this way, the benefits are demonstrated of adding volume scattering particles or a hemispherical extraction dome to the LED package. The best configuration in terms of luminous efficacy, however, is one where the red QDs are deposited in the recycling cavity, while the green QDs are incorporated in the extraction dome. Using this configuration with green and red InP/ZnSe/ZnS QDs with a PLQY of 75% and 65% respectively, luminous efficacy of 102 lm/W was realized for white light with a CCT of 3000 K.