A new model (CUJET3.0) of jet quenching in nuclear collisions coupled to bulk data constrained (VISH2+1D) viscous hydrodynamic backgrounds is constructed by generalizing the perturbative QCD based (CUJET2.0) model to include two complementary non-perturbative chromodynamical features of the QCD confinement cross-over phase transition near T c ≈ 160 MeV: (1) the suppression of quark and gluon chromo-electric-charged (cec) degrees of freedom and (2) the emergence of chromo-magnetic-monopole (cmm) degrees of freedom. Such a semi Quark Gluon Monopole Plasma (sQGMP) microscopic scenario is tested by comparing predictions of the leading hadron nuclear modification factors, R h AA (p T > 10GeV/c, √ s), and their azimuthal elliptic asymmetry v h 2 (p T > 10GeV/c, √ s) with available data on h = π, D, B jet fragments from nuclear collisions at RHIC( √ s = 0.2 ATeV) and LHC( √ s=2.76 ATeV). The cmm degrees of freedom in the sQGMP model near T c are shown to solve robustly the long standing R AA vs v 2 puzzle by predicting a maximum of the jet quenching parameter fieldq(E, T )/T 3 near T c . The robustness of CUJET3.0 model to a number of theoretical uncertainties is critically tested. Moreover the consistency of jet quenching with observed bulk perfect fluidity is demonstrated by extrapolating the sQGMPq down to thermal energy E ∼ 3T scales and showing that the sQGMP shear viscosity to entropy density ratio η/s ≈ T 3 /q falls close to the unitarity bound, 1/4π, in the range (1−2)T c . Detailed comparisons of the CUJET2.0 and CUJET3.0 models reveal the fact that remarkably differentq(T ) dependence could be consistent with the same R AA data and could only be distinguished by anisotropy observables. These findings demonstrate clearly the inadequacy of focusing on the jet path averaged quantity q as the only relevant medium property to characterize jet quenching, and point to the crucial roles of other essential factors beyond just the q , such as the chromo electric and magnetic composition of the plasma, the screening masses and the running couplings at multiple scales which all strongly influence jet energy loss.