We study a six-species Lotka-Volterra type system on different two-dimensional lattices when each species has two superior and two inferior partners. The invasion rates from predator sites to a randomly chosen neighboring prey's site depend on the predator-prey pair, whereby cyclic symmetries within the two three-species defensive alliances are conserved. Monte Carlo simulations reveal an unexpected non-monotonous dependence of alliance survival on the difference of alliance-specific invasion rates. The invasion probabilities are supplemented by Gaussian noise and conditions are identified that warrant the largest impact of noise on the evolutionary process. Our findings are conceptually related to the coherence resonance phenomenon in dynamical systems via the mechanism of threshold duality that is not limited to predator-prey cyclical interactions, but may apply to models of evolutionary game theory as well, thus indicating its applicability in several different fields of research.