The Asymmetric Traveling Salesman Problem (ATSP) is a generalization of the well-known NP-hard Traveling Salesman Problem (TSP), where edge costs depend on the direction of travel. While recent learning-based solvers for TSP use machine-learned heatmaps to guide Monte Carlo Tree Search (MCTS), we find that MCTS alone drives most of the performance, with heatmaps offering limited standalone value. Moreover, existing MCTS methods are largely restricted to 2D Euclidean TSPs, limiting real-world applicability. To address these gaps, we propose a new model combining an autoencoder and Graph Convolutional Network (GCN) to generate more informative heatmaps. We also design a tailored MCTS pipeline for ATSP, overcoming limitations of prior frameworks. Our approach achieves state-of-the-art results among learning-based methods on ATSP with low inference-time cost.