This paper considers real-time cluster-based wireless sensor networks where the nodes harvest energy from the environment. We target performance sensitive applications that have to collectively send their information to cluster head by a predefined deadline, such as in distributed real-time monitoring and detection. The nodes are equipped with Dynamic Modulation Scaling (DMS) capable wireless radios. The problem is to determine the time slots and modulation levels that will be used by each node while communicating with the cluster-head in order to achieve energy-neutral (perpetual) operation and maximize energy reserves. We propose a solution that adjusts underlying TDMA slots that enables high energy nodes to compensate by transmitting faster producing larger slack for dark nodes, while meeting the performance constraint. We present an optimal mixed integer linear programming based solution. We also develop fast heuristics that are shown to provide approximate solutions through comprehensive experiments with actual solar energy harvesting profiles.