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New in vitro measurements from two human donors for both steady and transient hemorheology are presented that are particularly suited for testing thixotropic and viscoelastic models for human blood and are made available to the community along with the relevant blood physiology. This more complete data set is analyzed within the context of recent thixo-elasto-visco-plastic models, and we improve upon the Horner-Armstrong-Wagner-Beris (HAWB) model to better model transient hemorheology. The improved model features an additional viscoelastic equation for the red blood cell rouleaux within blood, along with simplifications to the structure kinetics equation. The resulting model is fit to additional experimental data on human whole blood for a step shear change and steady shear experiments, and the corresponding parameter values are used to predict oscillatory shear moduli, transient large amplitude oscillatory shear, and unidirectional large amplitude oscillatory shear data. The modified HAWB model shows significant improvement in fitting and predicting the experimental data. Specifically, a significant overshoot is captured in step shear changes from a low shear rate to a moderate shear rate, and a plateau for the storage modulus is observed at low frequencies. Highly nonlinear behavior is observed for the third harmonic in unidirectional large amplitude oscillatory shear in the form of multiple extremum separated widely in frequency, which can be identified with the two dominant mechanisms for generating viscoelasticity in human blood, namely, rouleaux structuring and red blood cell deformation. We also discuss the potential applications and difficulties associated with the constitutive modeling of transient blood rheology and provide insight into microstructural sources of the stress contributions to the bulk flow behavior. [ABSTRACT FROM AUTHOR]