The power efficiency, spectral characteristics, and output directionality of light emitting diodes (LEDs) used for lighting and video display may be tailored by integrating nanostructures that interact with photon emitters. In this work, we demonstrate an approach in which visible-wavelength-emitting quantum dots (QDs) are integrated within a polymer-based photonic crystal (PC) and excited by an ultraviolet-emitting LED. The PC design incorporates two interleaved regions, each with distinct periods in orthogonal directions. The structure enables simultaneous resonant coupling of ultraviolet excitation photons to the QDs and visible QD emission at two different wavelengths to efficiently extract photons normal to the PC surface. The combined excitation and extraction enhancements result in a 5.8X increase in the QD output intensity. Further, we demonstrate multiple QD-doped PCs combined on a single surface to optimally couple with distinct populations of QDs, offering a means for blending color output and directionality of multiple wavelengths. Devices are fabricated upon flexible plastic surfaces by a manufacturable replica molding approach.