[indigochill]

My team is in a somewhat similar position relative to our company. I like to think of Jira as an interface for management (and in our case, internal customers) to create and manage high-level requests and priorities. Then our team internally creates Trello cards for the actual tasks that need to be done because we find it significantly more efficient than Jira. On our current project, the ratio of Trello cards to Jira tickets is ~15.

As long as we also keep Jira reasonably current with the status of the project, Management's fine with however we want to track our work internally. YMMV.