Molecular excitons play a central role in natural and artificial light harvesting, organic electronics, and nanoscale computing. The structure and dynamics of molecular excitons, critical to each application, are sensitively governed by molecular packing. Deoxyribonucleic acid (DNA) templating is a powerful approach that enables controlled aggregation via sub-nanometer positioning of molecular dyes. However, finer sub-Angstrom control of dye packing is needed to tailor excitonic properties for specific applications. Here, we show that adding rotaxane rings to squaraine dyes templated with DNA promotes an elusive oblique packing arrangement with highly desirable optical properties. Specifically, dimers of these squaraine:rotaxanes exhibit an absorption spectrum with near-equal intensity excitonically split absorption bands. Theoretical analysis indicates that the transitions are mostly electronic in nature and only have similar intensities over a narrow range of packing angles. Compared with squaraine dimers, squaraine:rotaxane dimers also exhibit extended excited-state lifetimes and less structural heterogeneity. The approach proposed here may be generally useful for optimizing excitonic materials for a variety of applications ranging from solar energy conversion to quantum information science.