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An attractive strategy to improve the energy transfer properties of synthetic dye networks is to optimize the excitonic coupling between the dyes to increase energy transfer rates. To explore this possibility, we investigate the use of J-like cyanine dye dimers (Cy3 and Cy5 dimers) on DNA duplexes as energy transfer relays in molecular photonic wires. This approach is based on using the collective emission dipole of a J-dimer to enhance the FRET rate between the dimer relay and a remote acceptor dye. Experimentally, we find that in room temperature aqueous buffer conditions the dimer relay provided no benefit in energy transfer quantum yield relative to a simple monomer relay. Further investigation led us to determine that enhanced non-radiative relaxation, non-ideal dye orientation within the dimer, and unfavorable dye orientation between the dimer and the acceptor dye limit energy transfer through the dimer relay. We hypothesized that non-radiative relaxation was the largest factor, and demonstrated this by placing the sample in a viscous solvent or cooling the sample, which dramatically improved energy transfer through the J-like dimer relay. Similar to how the formation of DNA-templated J-like dimers has improved, the practical use of J-like dimers to optimize energy transfer quantum efficiency will require improvements in the ability to control orientation between dyes to reach its full potential.