We report results of a comprehensive global $\chi^2$ analysis of nuclear collision data from RHIC (0.2 ATeV), LHC1 (2.76 ATeV), and recent LHC2 (5.02 ATeV) energies using the updated CUJET framework. The framework consistently combines viscous hydrodynamic fields predicted by VISHNU2+1 (validated with soft $p_T<2$~GeV bulk observables) and the DGLV theory of jet elastic and inelastic energy loss generalized to QGP fluids with an sQGMP color structure, including effective semi-QGP color electric quark and gluon as well as emergent color magnetic monopole degrees of freedom constrained by lattice QCD data. We vary the two control parameters of the model (the maximum value of the running QCD coupling, $\alpha_c$, and the ratio $c_m$ of color magnetic to electric screening scales) and calculate the global $\chi^2(\alpha_c,c_m)$ compared with available jet fragment observables $(R_{AA}, v_2)$. A global $\chi^2$<2 minimum is found with $\alpha_c$≈0.9±0.1 and $c_m$≈0.25±0.03. Using CIBJET, the event-by-event (ebe) generalization of the CUJET framework, we show that ebe fluctuations in the initial conditions do not significantly alter our conclusions (except for v3). An important theoretical advantage of the CUJET and CIBJET frameworks is not only its global $\chi^2$consistency with jet fragment observables at RHIC and LHC and with non-perturbative lattice QCD data, but also its internal consistency of the constrained jet transport coefficient, $\hat{q}(E,T)/T^3$, with the near-perfect fluid viscosity to entropy ratio $(\eta/s \sim T^3/\hat{q}\sim 0.1-0.2)$ property of QCD fluids near $T_c$ needed to account for the low $p_T<2$ GeV flow observables. Predictions for future tests at LHC with 5.44 ATeV Xe + Xe and 5.02 ATeV Pb + Pb are also presented.