We consider the problem of mesh-pull based video broadcast in peer-to-peer networks. We propose a novel algorithm for constructing the distribution overlay, where peers are arranged in neighborhoods that exhibit similar latency values from the origin media server. We analyze the properties of the resulting mesh and show that it increases data sharing between neighbors, hence improves the system performance compared to random constructions. The nodes are further equipped with a novel streaming strategy that is built on utility-based packet scheduling and proportional resource sharing in order to fight against free-riders. The utility is driven by both the packet importance for the video quality the packet popularity within the peer neighborhood. Our simulation results show that the proposed protocols increase the performance of a mesh-pull P2P broadcast system. Significant improvements are registered relative to existing solutions in terms of average quality and average decoding rate due to the packet scheduling and the mesh construction algorithm. The latter provides further gains in performance in terms of frame-freeze and playback latency relative to a conventional approach where peer neighbors are selected at random. Corresponding gains in video quality are registered due to the improved continuity of the playback experience.