Recent work modeling the rheological behavior of thixo-elasto-viscoplastic (TEVP) materials such as human blood indicates that it has all of the hallmark features of a complex material, including shear-thinning, viscoelasticity, a yield stress, and thixotropy. After decades of modeling steady-state human blood rheological data, and the development of simple steady-state models, like the Casson and Herschel-Bulkley, the advancement and evolution of TEVP modeling to transient flow conditions now has reinvigorated interest. Using recently collected human blood rheological data, over a wide range of flow conditions from steady state to various oscillatory shear flows, we show and compare modeling efforts with the original and a viscoelasticity-enhanced version of the enhanced Apostolidis-Armstrong-Beris (EAAB) model. The viscoelasticity enhancement is then justified by its ability to improve predictions of small and large amplitude oscillatory shear as well as uni-directional oscillatory shear flow. The new viscoelastic parameter is then incorporated into a methodology to estimate the viscoelastic time scale of human blood. Lastly, we compare our new TEVP modeling approach with another recently developed TEVP model, mHAWB, for context.