We explore the origins of shear stress overshoots upon flow inception of main-chain thermotropic liquid crystalline polymers from a random polydomain initial condition. A simple polydomain simulation strategy, based on Ericksen's transversely isotropic fluid model, is capable of predicting a shear stress overshoot arising from the reorientation dynamics of domains toward a steady state flow aligned state. When model parameters are estimated using elementary molecular theories for semiflexible main-chain thermotropes, both the relative magnitude of the shear stress overshoot and the steady state ratio of first normal stress difference to shear stress are determined solely by the "tumbling" parameter, lambda. This implies a universal correlation between these two variables. We test this prediction against an extensive data set on semiflexible polyesters and find good qualitative agreement between model and experiment.