The morphology of a multicomponent polymer melt within self-consistent field theory (SCFT) is completely characterized by the spatial density distribution of the components. SCFT therefore assumes that the molecular conformations are fast variables that adopt their equilibrium statistics with respect to a given density distribution. There are multiple situations, e.g., the early stages of structure formation, where this assumption breaks down because the densities evolve significantly on the time scale of the single-chain relaxation. Here, we develop a SCFT that uses as slow variables both densities and the variance of the first, most slowly relaxing Rouse mode and we design a numerical scheme for its solution based on single-chain propagators. Applications to diblock and multiblock copolymers are presented.