We revisit the far from equilibrium escape problem across a fluctuating potential barrier that is driven by asymmetric, unbiased dichotomous noise. Our closed analytical solution for arbitrary noise strengths reveals new aspects of the so-called "resonant-activation" effect and leads to interesting implications regarding far from equilibrium or externally controlled chemical reaction processes. Specifically, a genuine asymmetry-induced variant of resonant activation within the constant intensity scaling scheme is discovered, and a new possibility to manipulate reaction rates and yields, as well as the balance between reactants and products, is put forward.