Transition-metal-ion-doped lead-free halide double perovskites are important near-infrared and visible phosphors, but ground-state Kohn-Sham level differences describe their localized d-d transition energies poorly, and explicit excited-state methods are costly for doped supercells containing tens to hundreds of atoms. Using the wide-gap host Cs₂NaScCl₆, whose band edges are weakly dispersive, we develop and test a constrained spin-polarization scheme. The exact-exchange fraction of a screened hybrid functional is calibrated to the experimental optical gap (4.74 eV), giving 13.2%. At a fixed atomic configuration, the net spin electron number (the difference between the numbers of spin-up and spin-down electrons) is set to its ground-state value minus one, a single self-consistent calculation is performed, and the emission energy is estimated from level differences of the dopant. The host sequence Cs₂AgInCl₆ → Cs₂Ag_0.5Na_0.5InCl₆ → Cs₂NaInCl₆ → Cs₂NaScCl₆ shows how Na and Sc substitution turn the valence-band maximum into a Cl 3p state and the conduction-band minimum into a localized Sc 3d state, so that dopant levels can be identified inside a wide gap. For Mn²⁺, the constraint corresponds to the Slater midpoint between the sextet ground state and the quartet excited state. In the charge-uncompensated supercells, where the constraint yields integer occupations, the average difference between the minority-spin t_2g levels and the empty majorityspin e_g level is 2.04 eV, and 2.08 eV with Li⁺ on the Na site, consistent with the orange-red Mn²⁺ emission near 2.0 eV reported for related chloride double perovskites; after charge compensation by an interstitial Li⁺, one minority-spin t_2g level and the majority-spin e_g level each become half occupied, forming the Slater midpoint configuration, and the midpoint read-out rises to 2.38 eV. For the spin-conserving Cr³⁺ emission, an empirical read-out taken as the difference between the half-occupied and fully occupied t_2g levels of the same spin channel gives 1.28 eV (969 nm), within 2% of the reported 950–970 nm emission, whereas the ground-state eg-t_2g level difference (3.23 eV) deviates strongly from experiment. The co-doped Sb³⁺ ion is the ultraviolet absorber and sensitizer; its A, B and C bands (dominated by ¹S₀ → ³P₁, ³P₂ and ¹P₁) are described by an exciton model including electron-hole exchange and spin-orbit coupling. Li⁺ on the Na site, about 9 Å from the transition-metal ion, barely changes the d-d read-outs but enhances the Sb-Mn electronic coupling, favouring Sb³⁺ →Mn²⁺ energy transfer; an interstitial Li⁺ 3.6–3.7 Å away donates an electron and lengthens the metal-Cl bonds, compensating Mn²⁺ but driving Cr away from the ³d₃ configuration of Cr³⁺. The scheme offers a low-cost alternative to multiconfigurational excitedstate calculations for rapidly comparing the emission energies of different local doping configurations in wide-gap hosts with a measured optical gap.