We reexamine the stability of hexagonally modulated layer (HML) and hexagonally perforated layer (HPL) morphologies in a number of block copolymer systems of low to moderate molecular weight. Using small-angle X-ray scattering and dynamic mechanical spectroscopy, we show that these structures are long-lived nonequilibrium states which convert to the bicontinuous gyroid (G) morphology upon isothermal annealing. Comparison of phase transition kinetics across chemically distinct systems spanning a wide range of molecular weights and monomeric friction coefficients reveals a composition dependence to these dynamics. This suggests effects associated with the mobility of individual chains are of lesser importance in explaining the apparent metastability of the HML and HPL structures: instead, the composition dependence of the transition mechanism appears to dominate the observed behavior. The revised phase behavior for these materials is in excellent agreement with mean-field predictions for diblock copolymer melts.