Global social and ecological challenges represent collective action problems requiring rapid and sufficient cooperation with pro-mitigation norms. Sociopolitical polarization hinders such cooperation. Prior agent-based models showed polarization emerges naturally in structured social networks and polarized cluster dissolution rate limits consensus formation rate. Here we study how guided link rewiring affects depolarization dynamics across synthetic and empirical (Facebook, Twitter) network topologies. We compare heuristic rewiring algorithms representing random meetings, mutual acquaintance introductions, and community bridging, alongside topology-based link recommender algorithms (Who to Follow and node2vec). Our heuristic algorithms all outperform Who to Follow in generating cooperative consensus. Homophilic rewiring generates cooperative consensus when agents can easily change opinions. However, heterophilic rewiring achieves this over broader conditions and can accelerate cooperative consensus formation by ~20%, including where up to 33% of the population experiences backfiring interactions. Heterophilic rewiring also vastly outperforms topology-based recommender algorithms. Random rewiring performed consistently well, achieving higher steady-state cooperation than seven out of eight more complex algorithms. Large disparities in steady-state cooperation for topology-based recommender systems highlight their volatility across network structures. Overall, our work reveals a subtle interplay between topology, rewiring algorithm and social depolarization, suggesting strong potential for carefully redesigning social networking technologies for social good.