Reliable Alzheimer's disease (AD) diagnosis increasingly relies on multimodal assessments combining structural Magnetic Resonance Imaging (MRI) and Electronic Health Records (EHR). However, deploying these models is bottlenecked by modality missingness, as MRI scans are expensive and frequently unavailable in many patient cohorts. Furthermore, synthesizing de novo 3D anatomical scans from sparse, high-dimensional tabular records is technically challenging and poses severe clinical risks. To address this, we introduce MIRAGE, a novel framework that reframes the missing-MRI problem as an anatomy-guided cross-modal latent distillation task. First, MIRAGE leverages a Biomedical Knowledge Graph (KG) and Graph Attention Networks to map heterogeneous EHR variables into a unified embedding space that can be propagated from cohorts with real MRIs to cohorts without them. To bridge the semantic gap and enforce physical spatial awareness, we employ a frozen pre-trained 3D U-Net decoder strictly as an auxiliary regularization engine. Supported by a novel cohort-aggregated skip feature compensation strategy, this decoder acts as a rigorous structural penalty, forcing 1D latent representations to encode biologically plausible, macro-level pathological semantics. By exclusively utilizing this distilled "diagnostic-surrogate" representation during inference, MIRAGE completely bypasses computationally expensive 3D voxel reconstruction. Experiments demonstrate that our framework successfully bridges the missing-modality gap, improving the AD classification rate by 13% compared to unimodal baselines in cohorts without real MRIs.