Motion planning, which is the problem of computing feasible paths through an environment for a movable object, has applications in many domains ranging from robotics, to intelligent CAD, to protein folding. The best methods for solving this PSPACE-hard problem are so-called sampling-based planners. Recent work introduced uniform spatial subdivision techniques for parallelizing sampling-based motion planning algorithms that scaled well. However, such methods are prone to load imbalance, particularly as the number of processors is increased, because planning time depends on region characteristics and, for most problems, the heterogeneity of the set of regions increases as the region size decreases. In this work, we introduce two techniques to address the problems of load imbalance in the parallelization of sampling-based motion planning algorithms: bulk-synchronous redistribution and an adaptive work- stealing approach. We show that applying these techniques to representatives of the two major classes of parallel sampling-based motion planning algorithms, probabilistic roadmaps and rapidly-exploring random trees, results in a more scalable and load-balanced computation on 3,000+ cores.