Here, we use a model approach, based on coarse-grained (CG) molecular dynamics simulations and theory, to elucidate the conditions and DNA sequence complexity necessary to achieve error-free, onepot self-assembly of 2D distinguishable blocks into arbitrary patterns. Our model suggests the existence of a domain in the temperature/misbinding diagram where complete error-free self-assembly is possible. We then analyze the interaction energies between sequences in DNA-brick experiments and uncover a multi-modal energy distribution. Utilizing this energy spectrum into our CG model allows us to propose a rational design scheme capable of generating collections of sequences with low misbinding. Moreover, such a framework can provide a quantitative estimate for the length, number, and complexity of DNA sequences needed to synthesize, and maximum size of, structures that can be self-assembled with high accuracy and yield. This optimization of DNA-guided 2D assembly can provide facile routes to achieve precise alignments of graphene and other nanosheets during liquid-phase processing, thereby potentially improving the electrical conductivity achievable in energy storage applications, among other benefits.