Custom API Action: Access Request Body
This is typically handled by adding a webhook endpoint to your extension.  The Mailchimp extension does this - see Webhook.php.

If you've already written your API action, it shouldn't be too tough to use a webhook to grab the data and push to API.

It sounds like maybe you're past this point, but https://lab.civicrm.org/dev/financial/issues/55 is an issue I raised to deal with handling POST data stored as JSON.