Centralized reactive orchestration in Low Earth Orbit (LEO) networks struggles with heavy-tailed traffic surges that trigger signaling storms and topology instability. To address this challenge, we develop a LEO-specific predictive resource allocation framework that integrates spectral-aware distributional forecasting with risk-aware allocation. The forecasting module pairs cascaded dual-scale Exponential Moving Average (EMA) decomposition with a direct multi-step decoder to suppress autoregressive error accumulation. A Spectral Penalty operating in the frequency domain enhances sensitivity to orbital harmonics, while nonuniform quantization yields calibrated probabilistic bounds that preserve heavy-tailed characteristics. On the allocation side, the predictive standard deviation serves as an endogenous risk index amplified by service priority to form a capacity bound that is explicitly aware of risk. A companion demand model structurally reserves a fixed control plane bandwidth floor, insulating signaling from data plane congestion. Simulation results show that the forecasting module reduces the Continuous Ranked Probability Score (CRPS) by up to 5.9% relative to the strongest compared distributional baseline across prediction horizons of 30–105 min. Under a 300% traffic shock, the distributed allocation mechanism maintains 99.99% satisfaction for the highest priority service class and keeps control plane overflow below 0.05%. Lower-priority traffic is curtailed through compression governed by priority, and the per-node memory consumption is sufficiently low for deployment on current onboard satellite processors.