The proliferation of wireless mobile devices encourages research into their employment to form delay tolerant networks (DTN) for such applications as disaster response, military communications, and crowdsourcing. Within a DTN, messages are exchanged between nodes following a store-carry-forward paradigm, which is notably susceptible to congestion and can lead to a crippling in network performance. A DTN’s time-dynamic topology departs from traditional network definitions in its unpredictable and volatile nature, thus prohibiting the effective adoption of traditional network solutions to this problem. In this paper, the Catora system is proposed as a multi-copy message exchange and buffer management system designed to both aid in the delivery of prioritized messages and mitigate congestion and its degradation. Operating around the distinct ordering of messages for transfer, delivery, and deletion, Catora propagates messages so as to balance their dissemination, hasten the delivery of high priority messages, and avoid congestion through strategic buffer management. Simulations using two real-world datasets demonstrate Catora’s capability to quickly deliver more messages at reduced overhead costs when compared to benchmarks and the state-of-the-art, even when the network suffers from congestion.