The efficacy of Doppler laser cooling in radio-frequency Paul traps depends sensitively on the mutual orientation of the cooling-laser axis and the crystal principal axes, yet this angular dependence has not been systematically investigated across structural phase transitions. We report a comprehensive charged-particle dynamics study of a 50-ion ⁸⁸Sr⁺ Coulomb crystal for end-cap voltages U_ec = 0.5–200 V (Mathieu q = 0.2) and laser polar angles θ = 0°–90° in 5° steps, spanning the linear-chain, zigzag-ribbon, and prolate-ellipsoid regimes. By employing energy-decomposition thermometry to separately quantify secular and micromotion temperatures, we find that the cooling rate γ increases overall with trap anisotropy α—from 7.6 ms⁻¹ in the linear and near-linear crystals to ≈16.6 ms⁻¹ in the ellipsoids—while the equilibrium temperature drops from 160 mK at U_ec = 0.5 V (angle average) to ≈3.6 mK in the optimally cooled ellipsoids. The temperature drop is driven primarily by the structural phase transition itself: as the crystal buckles from one-dimensional chains into multi-dimensional zigzag and ellipsoid morphologies, efficient Coulomb thermalization between axial and radial modes eliminates the radial cooling bottleneck, causing T_eq to saturate near 7 T_D—well above the Doppler limit but almost independent of the precise cooling rate. The anisotropy ratio R = T_radial/T_axial drops from R ≈ 130 in the one-dimensional chain to R ≈ 1–2 in the ellipsoids, reflecting the progressive elimination of the radial cooling bottleneck by three-dimensional Coulomb thermalization. In linear chains the temperature anisotropy T_radial/T_axial exceeds 10 at θ = 0° and decays toward isotropy as θ increases; zigzag and ellipsoid structures are far less sensitive to θ because three-dimensional Coulomb thermalization randomizes directional energy flow. The optimal cooling angle shifts from ≈10° in the one-dimensional chain to 45°–50° in the higher-dimensional structures, indicating that strong inter-ion coupling progressively relaxes the need for direct radial laser damping. These results establish a predictive map for cooling-protocol optimization in scalable ion-trap quantum processors.