We developed a common algorithmic solution addressing the problem of resource-constrained outreach encountered by social change organizations with different missions and operations: Breaking Ground -- an organization that helps individuals experiencing homelessness in New York transition to permanent housing and Leket -- the national food bank of Israel that rescues food from farms and elsewhere to feed the hungry. Specifically, we developed an estimation and optimization approach for partially-observed episodic restless bandits under $k$-step transitions. The results show that our Thompson sampling with Markov chain recovery (via Stein variational gradient descent) algorithm significantly outperforms baselines for the problems of both organizations. We carried out this work in a prospective manner with the express goal of devising a flexible-enough but also useful-enough solution that can help overcome a lack of sustainable impact in data science for social good.