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Recent theoretical investigations have indicated that rapid optical cycling should be feasible in complex polyatomic molecules with diverse constituents, geometries and symmetries. However, as a composite molecular mass grows, so does the required number of photon scattering events necessary to decelerate and confine molecular beams using laser light. Utilizing coherent momentum exchange between light fields and molecules can suppress spontaneous emission and significantly reduce experimental complexity for slowing and trapping. Working with BaH as a test species, we have identified a robust, experimentally viable configuration to achieve large molasses-like cooling forces for molecules using polychromatic optical fields addressing both $X-A$ and $X-B$ electronic transitions, simultaneously. Using numerical solutions of the time-dependent density matrix as well as Monte Carlo simulations, we demonstrate that creation of Suppressed Emission Rate (SupER) molasses with large capture velocities ($\sim 40$ m/s) is generically feasible for polyatomic molecules of increasing complexity that have an optical cycling center. Proposed SupER molasses are anticipated to not only extend quantum control to novel molecular species with abundant vibrational decay channels, but also significantly increase trapped densities for previously laser-cooled diatomic and triatomic species.