Long-range ordering of DNA crossover tiles with blunt ends on lipid bilayers is investigated using atomic force microscopy. "Blunt-ended" tiles do not have single-stranded complementary ends, and thus instead of assembling via base-pairing, they can interact by π-stacking of their duplex ends. This work demonstrates that the balance of base π-stacking interactions between the ends of DNA duplexes, cholesterol-mediated DNA anchoring, and electrostatic DNA binding to supported lipid bilayers (SLBs) presents an opportunity to build dynamic materials with long-range order on a soft support. The tiles are shown to organize into novel tunable surface packing morphologies on the micrometer scale. This work focuses on three-point star (3PS) tiles that are either unmodified or modified with a cholesterol unit and investigates their interactions on supported lipid bilayers. On fluid bilayers, the cholesterol tiles form extended hexagonal arrays with few defects, while the unmodified tiles do not bind. In contrast, both modified and unmodified tiles bind to gel-phase bilayers and produce arrays of new organized morphologies. With increasing tile concentration, we observe a range of motifs, that progressively favor tile-tile packing over duplex-end π-stacking. These structures can selectively pattern domains of phase-separated lipid bilayers, and the patterning is also observed for four-arm cross-tiles. Dynamic blunt end contacts promote error correction and network reconfiguration to maximize favorable interactions with the substrate and are required for the observed tile organization. These results suggest that small blunt-ended tiles can be used as a platform to organize oligonucleotides, nanoparticles, and proteins into extensive networks at the interface with biologically relevant membrane systems or other soft surface materials for applications in cellular recognition, plasmonics, light harvesting, model systems for membrane protein assemblies, or analytical devices.