We study a restrictive three-family realization of quark–lepton complementarity (QLC) in which the non-trivial correlation matrix is an exactly unitary rigid deformation of tri-bimaximal mixing. In a canonical real TBM frame the deformation is a rotation about $n_{gg}=(2,1,2{)}^T/3$ with ${\alpha }_{gg}=-3{\theta }_C/4$, giving $U_{\rm PMNS}=V_{\rm CKM}^{\dagger}U_{\rm TBM}R_{n_{gg}}(-3\theta_C/4)$. Once this structural choice is fixed, the Dirac lepton-mixing sector contains no new continuous parameter. With the 2025 Particle Data Group CKM fit the construction predicts ${\theta }_{12}={33.29}^{\circ }$, ${\theta }_{13}={8.46}^{\circ }$, ${\theta }_{23}={49.19}^{\circ }$, and $\delta_{\rm CP}=180.79^\circ$. We show explicitly that the near-CP-conserving prediction relies not only on the reality of the deformation but also on phase alignment: a generic relative $1$–$2$ charged-lepton/down-quark mismatch phase produces $J_{\rm CP}^{\ell}=\lambda\sin\phi_2/6+\mathcal{O}(\lambda^2\sin\phi_2,\lambda^3)$, whereas the fully aligned limit recovers $J_{\rm CP}^{\ell}=-A\eta\lambda^3/6+\mathcal{O}(\lambda^4)$. An exhaustive retrospective scan over all primitive-integer axes and reduced rational Cabibbo coefficients with $C_1=|a|+|b|+|c|+p+q\le 12$ contains 9018 candidates and ranks $(2,1,2),3/4$ first for both 2016 and 2018 inputs; the rank-one result persists under several alternative complete complexity sublevel sets, while larger discrete classes contain better-fitting but more complicated candidates. For the fixed $(2,1,2)$ axis the continuous optimum is $r_{\rm BF}=0.74941$. We distinguish the unitary-similarity law of the flavor generator from Majorana congruence transformations and show that the mass eigenframe admits both normal and inverted ordering. Present NuFIT 6.1 data favor the normal-ordering realization, while the upper-octant atmospheric angle and near-$\pi$ Dirac phase remain direct falsifiability targets.