As billions of people rely on end-to-end encrypted messaging, the exposure of metadata, such as communication timing and participant relationships, continues to deanonymize users. Asynchronous metadata-hiding solutions with strong cryptographic guarantees have historically been bottlenecked by quadratic$O(N^{2})$server computation in the number of users$N$due to reliance on private information retrieval (PIR). We present Myco, a metadata-private messaging system that preserves strong cryptographic guarantees while achieving$O(N\log^{2}N)$efficiency. To achieve this, we depart from PIR and instead introduce an oblivious data structure through which senders and receivers privately communicate. To unlink reads and writes, we instantiate Myco in an asymmetric two-server distributed-trust model where clients write messages to one server tasked with obliviously transmitting these messages to another server, from which clients read. Myco achieves throughput improvements of up to 302x over multi-server and 2,219x over single-server state-of-the-art systems based on PIR.