State-of-the-art 6-DoF grasp generators excel on tabletop benchmarks with overhead cameras but struggle in frontal grasping scenarios on low-cost manipulators with constrained workspaces, where kinematic limits and approach-direction constraints cause high failure rates. We address this challenge for the Unitree Z1 arm by proposing MVB-Grasp, a novel grasping stack that injects a Minimum Volume Bounding Box (MVBB) geometric prior into diffusion-based grasp generation to dramatically improve success rates in frontal, workspace-constrained settings. Our key scientific contributions are threefold: (i) an MVBB-based geometric filter that exploits oriented bounding-box face normals to reject grasps approaching through the table or misaligned with accessible object faces in O(N) time; (ii) a combined re-scoring function that blends learned discriminator scores with face-alignment geometry α=0.85, specifically calibrated for the Z1's frontal workspace and kinematic constraints; and (iii) a systematic MuJoCo evaluation protocol measuring grasp success across object types, distances, lateral positions, and pitch orientations to validate embodiment-specific performance. We implement MVB-Grasp on a Unitree Z1 arm with an Intel RealSense D405 camera, integrating YOLOv8 object detection, GraspGen for candidate generation, Principal Component Analysis (PCA)-based MVBB fitting, and inverse-kinematics trajectory planning. Experiments across 81 MuJoCo episodes (cylinder, asymmetric box, waterbottle) demonstrate that MVB-Grasp achieves 59.3% success versus 24.7% for vanilla GraspGen, a 2.4x improvement, by filtering geometrically infeasible candidates and prioritizing face-aligned grasps suited to the Z1's frontal approach constraints. Real-world trials confirm that the MVBB prior substantially improves grasp reliability on constrained, low-cost manipulators without requiring model retraining.