Swarm robotics (SR) offers promising solutions to real-world problems that can be modeled as foraging tasks, e.g. disaster/trash cleanup or object gathering for construction. Yet current SR foraging approaches make limiting assumptions that restrict their applicability to selected real-world environments. We propose an improved self-organized task allocation method based on task partitioning that removes restrictions such as: (1) a priori knowledge of foraging environment, and (2) strict limitations on intermediate drop/pickup site behavior. With experiments in simulation, we show that under the proposed constraint relaxation, our approach still provides performance increases when compared to an unpartitioned strategy within some combinations of swarm sizes, robot capabilities, and environmental conditions. This work broadens the applicability of SR foraging approaches, showing that they can be effective under ideal conditions while continuing to perform robustly in more volatile/challenging environments.