Reliable 3D-2D alignment between intraoral scan (IOS) models and lateral cephalometric radiographs is critical for orthodontic diagnosis, yet conventional intensity-driven registration methods struggle under real clinical conditions, where cephalograms exhibit projective magnification, geometric distortion, low-contrast dental crowns, and acquisition-dependent variation. These factors hinder the stability of appearance-based similarity metrics and often lead to convergence failures or anatomically implausible alignments. To address these limitations, we propose DentalSCR, a pose-stable, contour-guided framework for accurate and interpretable silhouette-to-contour registration. Our method first constructs a U-Midline Dental Axis (UMDA) to establish a unified cross-arch anatomical coordinate system, thereby stabilizing initialization and standardizing projection geometry across cases. Using this reference frame, we generate radiograph-like projections via a surface-based DRR formulation with coronal-axis perspective and Gaussian splatting, which preserves clinical source-object-detector magnification and emphasizes external silhouettes. Registration is then formulated as a 2D similarity transform optimized with a symmetric bidirectional Chamfer distance under a hierarchical coarse-to-fine schedule, enabling both large capture range and subpixel-level contour agreement. We evaluate DentalSCR on 34 expert-annotated clinical cases. Experimental results demonstrate substantial reductions in landmark error-particularly at posterior teeth-tighter dispersion on the lower jaw, and low Chamfer and controlled Hausdorff distances at the curve level. These findings indicate that DentalSCR robustly handles real-world cephalograms and delivers high-fidelity, clinically inspectable 3D--2D alignment, outperforming conventional baselines.