Genesys Cloud webhook retry limit hit - implementing dead letter queue

Our internal endpoint started returning 503s, and Genesys eventually stopped retrying after the default limit. I need to implement a dead letter queue to catch these failed deliveries for manual replay, but the webhook subscription config doesn’t seem to expose a DLQ endpoint field in the API docs.

{
 "status": 429,
 "message": "Webhook delivery failed after 10 retries"
}

Is there a way to configure this via the API, or do I have to spin up a separate listener service?