Forecasting geopolitical conflict from data sources like the Global Database of Events, Language, and Tone (GDELT) is a critical challenge for national security. The inherent sparsity, burstiness, and overdispersion of such data cause standard deep learning models, including the Temporal Fusion Transformer (TFT), to produce unreliable long-horizon predictions. We introduce STFT-VNNGP, a hybrid architecture that won the 2023 Algorithms for Threat Detection (ATD) competition by overcoming these limitations. Designed to bridge this gap, our model employs a two-stage process: first, a TFT captures complex temporal dynamics to generate multi-quantile forecasts. These quantiles then serve as informed inputs for a Variational Nearest Neighbor Gaussian Process (VNNGP), which performs principled spatiotemporal smoothing and uncertainty quantification. In a case study forecasting conflict dynamics in the Middle East and the U.S., STFT-VNNGP consistently outperforms a standalone TFT, showing a superior ability to predict the timing and magnitude of bursty event periods, particularly at long-range horizons. This work offers a robust framework for generating more reliable and actionable intelligence from challenging event data, with all code and workflows made publicly available to ensure reproducibility.