The classical domination numbers of cylindrical grids P3 ⊔ Cn and P4 ⊔ Cn, along with the established bounds for P5 ⊔ Cn, were previously proved by Nandi, Parui and Adhikari (2011); they are not new theorems of this work. Instead, this study supplies a fully specified, independently executable finite-state benchmark for ordinary domination and three related parameters. We prove the exact correspondence between dominating sets and minimum-weight closed walks in a subset-pair transfer graph, explicitly stating cyclic initialization and terminal conditions. Exhaustive transfer calculations determine ordinary domination for k ∈ {3,4,5} and 3 ≤ n ≤ 40, with selected instances cross-checked using an independent mixed-integer linear programming (MILP) formulation. We also compute numerical profiles for total, independent, and strong domination for n = 3 to 10. The results reproduce prior formulas, correct incomplete notation, and emphasize finite certification and reproducibility.