Quantitative measurements of molecular orientation and rheology are reported for various transient shear flows of a nematic semiflexible copolyether. Unlike the case of lyotropic liquid crystalline polymers (LCPs), whose structure and rheology in shear are dominated by director tumbling, this material exhibits flow aligning behavior. The observed behavior is quite similar to that seen in a copolyester that we have recently studied [Ugaz and Burghardt (1998)], suggesting that flow aligning dynamics may predominate in main-chain thermotropes that incorporate significant chain flexibility. Since the flow aligning regime has received little attention in previous attempts to model the rheology of textured, polydomain LCPs, we attempt to determine whether available models are capable of predicting the orientation and stress response of this class of LCP. We first examine the predictions of the polydomain Ericksen model, an adaptation of Ericksen's transversely isotropic fluid model which accounts for the polydomain distribution of director orientation while neglecting distortional elasticity. This simple model captures a number of qualitative and quantitative features associated with the evolution of orientation and stress during shear flow inception, but cannot cope with reversing flows. To consider the possible role of distortional elasticity in the re-orientation dynamics upon reversal, we evaluate the mesoscopically averaged domain theory of Larson and Doi [Larson and Doi (1991)], which incorporates a phenomenological description of distortional elastic effects. To date, their approach to account for polydomain structure has only been applied to describe tumbling LCPs. We find that it captures the qualitative transient orientation response to flow reversals, but is less successful in describing the evolution of stresses. This is linked to the decoupling approximation adopted during the model's development. Finally, a modified polydomain Ericksen model is introduced that provides some of the benefits of the Larson-Doi model while offering more realistic stress predictions.