Many modern systems for speaker diarization, such as the recently-developed VBx approach, rely on clustering of DNN speaker embeddings followed by resegmentation. Two problems with this approach are that the DNN is not directly optimized for this task, and the parameters need significant retuning for different applications. We have recently presented progress in this direction with a Leave-One-Out Gaussian PLDA (LGP) clustering algorithm and an approach to training the DNN such that embeddings directly optimize performance of this scoring method. This paper presents a new two-pass version of this system, where the second pass uses finer time resolution to significantly improve overall performance. For the Callhome corpus, we achieve the first published error rate below 4% without any task-dependent parameter tuning. We also show significant progress towards a robust single solution for multiple diarization tasks.