We study the crystallization of nearly-hard sphere colloids induced by the addition of non-adsorbing polymers, using large-scale molecular dynamics and Monte Carlo simulations. Unlike similar crystals nucleated from pure systems, our results reveal thermodynamically stable, long range ordered hexagonally close packed (HCP) structures free of significant stacking faults for a range of polymer chain lengths. Polymers outside this range induce random hexagonally close packed (rHCP) structures with no long-range symmetry, consistent with experiments on pure systems under both terrestrial and microgravity [1]. These structures are traditionally believed to anneal into a face-centered cubic (FCC) state at long times owing to its marginally higher entropy in the case of pure colloid systems [2]. However, our simulations reveal the FCC state is thermodynamically suppressed in the binary case for chains of a certain length. This effect can be rationalized by considering the differences in interstitial void symmetry between the polymorphs, which control how polymers distribute themselves inside each crystal. We show how these differences can be used in concert with the geometry and thermal interactions of an arbitrary depletant to control the most stable polymorph. The resulting set of intelligent design principles suggests how polymers, or other soft materials, can be used as simple structure directing agents that derive their utility primarily from the free energy of confinement in the resulting porous structures, even when they are not the primary driving force for the self-assembly of these structures. We furthermore discuss the use of such agents in directing other extended crystal structures such as binary superlattices.