Using the CUJET3=DGLV+VISHNU jet-medium interaction framework, we show that dijet azimuthal acoplanarity in high energy A + A collisions is sensitive to possible non-perturbative enhancement of the jet transport coefficient, qˆ(T,E), in the QCD crossover temperature T ∼ 150–300 MeV range. With jet-medium couplings constrained by global RHIC& LHC χ2 fits to nuclear modification data on RAA(pT > 20) GeV, we compare predictions of the medium induced dijet transverse momentum squared, Qs2∼〈qˆL〉∼Δϕ2E2, in two models of the temperature, T, and jet energy E dependence of the jet medium transport coefficient, qˆ(T,E)). In one model, wQGP, the chromo degrees of freedom (dof) are approximated by a perturbative dielectric gas of quark and gluons dof. In the second model, sQGMP, we consider a nonperturbative partially confined semi-Quark-Gluon-Monopole-Plasma with emergent color magnetic dof constrained by lattice QCD data. Unlike the slow variation of the scaled jet transport coefficient, qˆwQGP/T3, the sQGMP model qˆsQGMP/T3 features a sharp maximum in the QCD confinement crossover T range. We show that the dijet path averaged medium induced azimuthal acoplanarity, Δϕ2, in sQGMP is robustly ∼ 2 times larger than in perturbative wQGP. even though the radiative energy loss in both models is very similar as needed to fit the same RAA data. Future A+A dijet acoplanarity measurements constrained together with single jet RAA and νn measurements therefore appears to be a promising strategy to search for possible signatures of critical opalescence like phenomena in the QCD confinement temperature range.