Architect: Calling a Common Module from multiple inbound flows

How do we actually trigger a shared Common Module from different inbound call flows without hardcoding the logic?

We’ve got three separate flows routing to the same queue, and they all need to run the same CRM lookup before transferring. I tried using a Data Action to call the module endpoint, but it just hangs and times out with a 504.

Is there a specific API pattern or JSON payload structure for invoking a reusable module instance dynamically?