We identify inefficient network topologies and resource allocation mechanisms to be the key obstacles toward adopting present P2P systems as the platform of choice for delivering high-quality live multimedia content. To this end, we propose a comprehensive optimization framework that overcomes these challenges in a systematic manner. In particular, we design a delay-based network construction procedure that creates small-world topologies that provide for efficient data delivery routes and increased data sharing between peers in the network. Furthermore, we equip the nodes with a utility-based packet scheduling technique that maximizes the video quality at a receiving peer subject to available bandwidth resources while allowing for dissemination of less frequently encountered data in the network. Finally, we design an uplink sharing strategy that enables the peers to deal effectively with free-riders in the system. Through theoretical analysis and simulation experiments we demonstrate that the proposed protocols provide for substantial improvements in performance in mesh-pull based P2P live multimedia delivery. Specifically, significant gains are registered over existing solutions in terms of average video quality and decoding rate. The proposed mesh construction procedure provides further gains in performance in terms of reductions in frame-freeze and playback latency relative to the commonly employed approach of random peer neighbour selection. Corresponding gains in video quality for the media presentation are also registered due to the improved continuity of the playback experience.