Rod-like objects at high packing fractions can form smectic phases, where the rods break rotational and translational symmetry by forming lamellae. Smectic defects thereby include both discontinuities in the rod orientational order (disclinations), as well as in the positional order (dislocations). In this work, we use both experiments and simulations to probe how local and global geometrical frustrations affect defect formation in hard-rod smectics. We confine a particle-resolved, colloidal smectic within elliptical wells of varying size and shape for a smooth variation of the boundary curvature. We find that the rod orientation near a boundary — the anchoring — depends upon the boundary curvature, with an anchoring transition observed at a critical radius of curvature approximately twice the rod length. The anchoring controls the smectic defect structure. By analyzing local and global order parameters, and the topological charges and loops of networks made of the density maxima (rod centers) and density minima (rod ends), we quantify the amount of disclinations and dislocations formed with varying confinement geometry. More circular confinements, having only planar anchoring, promote disclinations, while more elliptical confinements, with antipodal regions of homeotropic anchoring, promote long-range smectic ordering and dislocation formation. Our findings demonstrate how geometrical constraints can control the anchoring and defect structures of liquid crystals - a principle that is applicable from molecular to colloidal length scales.