Despite the effectiveness of cosine scoring compared to classical Probabilistic Linear Discriminant Analysis (PLDA), structured generative models such as Toroidal Probabilistic Spherical Discriminant Analysis (T-PSDA) can still provide superior performance for DNN-based speaker verification. In this work we investigate the relationship between T-PSDA and an isotropic simplified PLDA (ISO-PLDA) model, and propose a novel approach that combines the ISO-PLDA Gaussian likelihood with the structured directional T-PSDA speaker characterization to obtain a Spherical-Gaussian (SG-TPSDA) model that is able to match and, in some cases, improve T-PSDA performance. Furthermore, we show how to extend both ISO-PLDA and SG-TPSDA to explicitly account for utterance duration. Our results on NIST and CN-Celeb data show that the proposed approach is effective and capable of leveraging duration information to further improve speaker verification accuracy.