Object detection in large, dense remote sensing imagery is difficult because targets are often small and arbitrarily oriented, and state-of-the-art detectors cannot process very large images directly without a reduction in accuracy. Tiling-based inference workflows mitigate the latter issue by running inference iteratively on overlapping tiles, but introduce pre- and postprocessing overhead for image tiling and Non-Maximum Suppression (NMS). We introduce local NMS, an asynchronous tile-wise postprocessing scheme. Local NMS runs in a separate subprocess in parallel to tile-wise inference and collects intermediate results enqueued by the inference process, immediately applying postprocessing. Intelligent reordering of tiles in a preprocessing step ensures optimal usage of computing resources. We assess our method using three state-of-the art object detection models for horizontal and oriented bounding box detection on two benchmark datasets containing large dense aerial and satellite images, DOTA-v2.0 and Izembek Lagoon Birds, stratifying by image size and average object density. Local NMS consistently reduces end-to-end runtime across models and datasets without significant impact on mAP. A maximum runtime reduction of 60.77% on large dense DOTA-v2.0 scenes could be achieved without modifying model architectures or retraining.