Sorry, but what's stopping the DLQ being a different topic on that Kafka - I get that the consumer(s) might be dead, preventing them from moving the message to the DLQ topic, but if that's the case then no messages are being consumed at all.
If the problem is that the consumers themselves cannot write to the DLQ, then that feels like either Kafka is dying (no more writes allowed) or the consumers have been misconfigured.
Edit: In fact there seems to be a self inflicted problem being created here - having the DLQ on a different system, whether it be another instance of Kafka, or Postgres, or what have you, is really just creating another point of failure.