We investigate vapor-deposited glasses of a phenanthroperylene ester, known to form an equilibrium hexagonal columnar phase, and show that liquid crystal-like order can be manipulated by the choice of deposition rate and substrate temperature during deposition. We find that rate-temperature superposition (RTS)-the equivalence of lowering the deposition rate and increasing the substrate temperature-can be used to predict and control the molecular orientation in vapor-deposited glasses over a wide range of substrate temperatures (0.75-1.0 T-g). This work extends RTS to a new structural motif, hexagonal columnar liquid crystal order, which is being explored for organic electronic applications. By several metrics, including the apparent average face-to-face nearest-neighbor distance, physical vapor deposition (PVD) glasses of the phenanthroperylene ester are as ordered as the glass prepared by cooling the equilibrium liquid crystal. By other measures, the PVD glasses are less ordered than the cooled liquid crystal. We explain the difference in the maximum attainable order with the existence of a gradient in molecular mobility at the free surface of a liquid crystal and its impact upon different mechanisms of structural rearrangement. This free surface equilibration mechanism explains the success of the RTS principle and provides guidance regarding the types of order most readily enhanced by vapor deposition. This work extends the applicability of RTS to include molecular systems with a diverse range of higher-order liquid-crystalline morphologies that could be useful for new organic electronic applications.