The continuous prediction and uncertainty quantification of unconfined compressive strength (UCS) and the fracture-related index of anisotropy (FRIA) are essential for optimizing drilling operations and hydraulic fracturing design in shale gas development. However, machine-learning-based log inversion often suffers from (1) spatial information leakage caused by autocorrelation in well logs, (2) implicit target contamination during multi-source data fusion, and (3) biased evaluation under random data splitting, which can overestimate apparent performance and underestimate extrapolation risk in deep heterogeneous intervals. To address these limitations, we propose a leakage-free, physics-constrained framework for predicting UCS and FRIA in the Weiyuan shale gas reservoir. Using 18,440 quality-controlled, depth-aligned samples, we adopt a contiguous depth-based split that preserves stratigraphic continuity while isolating training, validation, and test intervals to block spatial leakage. Under a strict leakage-free protocol, we evaluate single-task ensemble trees (STL-RF/HGB), a multi-task neural network (MTL-MLP), and a physics-informed variant (PINN-MLP) for deep-interval stabilization. The best model is target-dependent: STL-RF achieves R² = 0.984 for FRIA, whereas MTL-MLP attains R² = 0.874 for UCS. For deep formations (>4800 m), PINN-MLP with a depth-continuity constraint reduces deep-interval prediction error by 47.5%. Multi-seed experiments with 95% Student’s t confidence intervals further confirm robustness. Overall, the framework provides a reproducible workflow for continuous geomechanical-parameter prediction and risk-aware deployment in deep unconventional reservoirs.