A central puzzle in bilayer nickelate superconductors is why pressure, epitaxial strain, oxygen stoichiometry, and chemical substitution produce systematic but apparently different changes in the superconducting Tc. Here we show that these trends can be organized by a two-parameter control principle based on the d_(x²-y²)-orbital filling nₓ and the effective interlayer antiferromagnetic superexchange J_⊥. Starting from a physical picture in which the nearly half-filled d_(z²) orbital supplies localized spin correlations while the nearly quarter-filled d_(x²-y²) orbital carries superconductivity, we study an effective bilayer t-J_∥-J_⊥ model with parameters constrained by first-principles calculations. Combined slave-boson mean-field and density-matrix renormalization group calculations place realistic La₃Ni₂O₇ in an overdoped-cuprate-like regime where Tc is governed mainly by the pairing scale. In this regime, hole doping reduces nₓ and suppresses Tc, whereas tuning routes that enhance J_⊥ raise Tc. This framework accounts for the suppression by over-oxidation and Ca/Sr substitution, the half-dome oxygen-stoichiometry response in the film, the enhancement by Nd/Sm substitution in the pressurized bulk, the right-triangle-like pressure dependence in the bulk, and the enhancement by compressive strain in the film. It also separates clean carrier doping from oxygen-vacancy tuning: clean electron doping mainly increases nₓ, whereas oxygen vacancies weaken the apical-oxygen-mediated exchange path and introduce disorder. This leads to a falsifiable materials-design prediction: clean electron doping should enhance the pairing scale if introduced without oxygen vacancies or strong pair-breaking disorder.