While recent advancements in generative AI and physics-informed inverse design have enabled the identification of optimized microstructures for target mechanical properties, a critical bottleneck remains: translating these virtual descriptors into actionable labsynthesis. To realize accelerated materials discovery, one must establish robust inverse Structure–Process–Composition (ISPC) linkages. This study proposes an automated ISPC pipeline that maps complex microstructural and textural features directly to alloy chemistry and extrusion parameters (temperature and velocity). Leveraging a comprehensive experimental dataset of over 115 extruded magnesium alloy specimens, we evaluate and compare three distinct high-dimensional feature extraction architectures for inverse modeling. The first approach utilizes a baseline of classical statistical descriptors, including Gram matrices and 3-point spatial correlations for morphology, coupled with Generalized Spherical Harmonic (GSH) coefficients for texture, reduced via manifold learning and regressed using Multi-output Gaussian Processes. The second approach represents the microstructural topology and orientation distribution as a unified 2D graph, employing an attention-based Graph Neural Network (GNN) to capture local and global spatial dependencies. The third approach utilizes a state-of-the-art dual-tower architecture, combining Vision Transformer (ViT) encoders with a Diffusion-based (SDXL-derived) latent space to produce highly compressed, context-aware embeddings. Our comparative analysis reveals that the dual-tower latent approach is superior for predicting complex material compositions, achieving an 11% improvement in Mean Absolute Percentage Error (MAPE) over the other approaches. Conversely, the Graph Neural Network architecture demonstrated higher fidelity in capturing the sensitivities of extrusion speed and temperature, outperforming the baseline by 8% in predicting extrusion speed and temperature. By integrating these models into a unified framework, we provide the "missing link" in the Integrated Computational Materials Engineering (ICME) chain, enabling a seamless transition from inverse property design to laboratory synthesis of high-performance magnesium alloys.