Your team has deployed a Claude-based ticket classification service that routes incoming developer support tickets to the correct engineering team. Three weeks in, developers on the platform team complain that urgent API outage tickets are arriving 8–12 minutes after the incident is first reported. Examining the architecture, you find the service is running on a 5-minute pull schedule against the ticketing system's REST API. A webhook integration is available from the ticketing platform but hasn't been implemented. What is the most appropriate architectural response?