We generalize our recent new ideas for the continuous startup shear rheology of entangled polymer liquids in the transient stress overshoot regime to formulate a theory for the full constitutive response and nonequilibrium dynamics over all time scales, deformation rates, and degrees of entanglement. The convective constraint release (CCR) idea that chain retraction locally triggers disentanglement in a shear-rate-dependent manner is significantly modified to be physically consistent with our nonclassical treatment of delayed retraction due to an entanglement grip force. A detailed numerical study of the predictions of the theory is presented for the full stress-strain response, scaling behavior of the stress overshoot and undershoot features, orientational stress, primitive path contour length dynamics, and nonequilibrium steady-state properties spanning the slow and fast nonlinear deformation regimes. For deformations slow enough there is little or no chain stretch, our results are qualitatively the same as in prior tube-based models. However, under fast deformation conditions, we make qualitatively new predictions for all rheological and dynamic properties that are not contained in any existing models. No-fit-parameter quantitative comparisons are made with experimental and simulation studies, and very good agreement is found; testable predictions are made. Strong connections between properties (stress and degree of chain stretch) at the overshoot and in the steady state are found, which suggests common physics exists at the elastic-viscous crossover (stress overshoot) and for long time flow associated with a delayed onset of primitive path retraction and emergence of CCR.