We report the results for Nuclear Magnetic Resonance (NMR) studies of monolayer (incommensurate solid) films of molecular hydrogen physisorbed on hexagonal boron nitride (BN). From the observation of clear structural changes in the NMR spectra, a phase diagram is mapped out for this system for ortho concentrations 0.32 < X < 0.745 and temperatures 0.05 < T < 4.2 K. Two distinct orientationally ordered phases are seen: an expected pinwheel structure (for high X) and an expected herringbone structure (for low X). The main peak splitting of the pinwheel spectra increases from 33 kHz to 61 kHz as X decreases. The main peak separation of the herringbone spectra remains the same (similar to 53 kHz), but the shoulder separation increases from 158 kHz to 188 kHz as X decreases. The transition from the pinwheel phase to the herringbone phase is continuous, indicating at most a weak first order transition.