Multi-agent path finding (MAPF) is the combinatorial problem of planning optimal collision-avoiding paths for multiple agents, with application to robotics, logistics, and transportation. Though many recent learning-based works have focused on large-scale combinatorial problems by guiding their decomposition into sequences of smaller subproblems, the combined spatiotemporal and time-restricted nature of MAPF poses a particular challenge for learning-based guidance of iterative approaches like large neighborhood search (LNS), which is already a state-of-the-art approach for MAPF even without learning. We address this challenge of neural-guided LNS for MAPF by designing an architecture which interleaves convolution and attention to efficiently represent MAPF subproblems, enabling practical guidance of LNS in benchmark settings. We demonstrate the speedup of our method over existing state-of-the-art LNS-based methods for MAPF as well as the robustness of our method to unseen settings. Our proposed method expands the horizon of effective deep learning-guided LNS methods into multi-path planning problems, and our proposed representation may be more broadly applicable for representing path-wise interactions.