In aqueous foams, the diffusive gas transfer among neighboring bubbles drives a coarsening process which is accompanied by intermittent rearrangements of the structure. Using time-resolved diffusing-wave spectroscopy, we probe the dynamics of these events as a function of the rigidity of the gas-liquid interfaces, liquid viscosity, bubble size, and confinement pressure. We present in detail two independent techniques for analyzing the light scattering data, from which we extract the rearrangement duration. Our results show that interfacial rheology has a major impact on this duration. In the case of low interfacial rigidity, the rearrangements strongly slow down as the pressure is decreased close to the value zero where the bubble packing unjams. In contrast, if the interfaces are rigid, rearrangement durations are independent of the confinement pressure in the same investigated range. Using scaling arguments, we discuss dissipation mechanisms that may explain the observed dependency of the rearrangement dynamics on foam structure, pressure, and physicochemical solution properties.