Currently, there is no way to differentiate integration custom payloads in Dialogflow CX like on Dialogflow ES. We created a feature request on your behalf and informed the appropriate internal team.
However, since LINE is the only integration that does not respond when there are custom payloads for other integrations in the fulfillment, a possible workaround for this issue is to export and restore your current agent to another agent dedicated for your LINE integration that only has LINE custom payloads in the fulfillment.