The dynamics of nanostructured soft materials crucially impact their associated macroscopic material properties, yet they are often difficult to measure due to spatiotemporal limitations of conventional instrumentation. Herein, we use X-ray photon correlation spectroscopy to directly observe particle-scale dynamics during grain growth and coarsening in a body-centered cubic-forming diblock polymer melt, with specific attention to the distribution of structural relaxation times associated with the interplanar (110) distance. Following sample quenching from the disordered state, these dynamical phenomena surprisingly exhibit little dependence on time and thermal quench depth. We posit that these relaxations stem from collective particle motions during grain rotation. We also observe unusual internally referenced heterodyne correlations, which enable measurements of speed distributions within the sample. These speeds are significantly slower and appear at much longer annealing times than those previously reported during grain nucleation and growth in microphase-separated block polymer melts. Drawing on analogies between polycrystalline hard and soft materials, we ascribe these speed distributions to misorientation-dependent grain boundary migration during ordered domain coarsening and anomalously fast, cooperative stringlike particle motion along the grain boundaries. Thus, these coherent X-ray measurements provide new opportunities to interrogate grain boundary structure and dynamics in polycrystalline soft materials.