We present an end-to-end deep network model that performs meeting diarization from single-channel audio recordings. End-to-end diarization models have the advantage of handling speaker overlap and enabling straightforward handling of discriminative training, unlike traditional clustering-based diarization methods. The proposed system is designed to handle meetings with unknown numbers of speakers, using variable-number permutation-invariant cross-entropy based loss functions. We introduce several components that appear to help with diarization performance, including a local convolutional network followed by a global self-attention module, multi-task transfer learning using a speaker identification component, and a sequential approach where the model is refined with a second stage. These are trained and validated on simulated meeting data based on LibriSpeech and LibriTTS datasets; final evaluations are done using LibriCSS, which consists of simulated meetings recorded using real acoustics via loudspeaker playback. The proposed model performs better than previously proposed end-to-end diarization models on these data.