It's easy to say you're doing agile by slapping scrum terminology on your process and having a standup every morning.
When I came on board we were in this trap. While big changes were needed it made sense to refine what was already working and save the full move away from a 'wagile' environment for the future.
We moved away from functionality and use cases and focused on Epics and User stories. Feature teams were arranged around epics and used user stories for planning, design and eventually made their way into the next sprint.
After a series of refinements to our "wagile" process, it was clear that we needed to abandon a much waterfall as possible.
Three concurrent sprints were always going on: Discovery (PM and UX), Planning (PM, UX, DEV, QA) and Active (DEV, QA).
Discovery - Research, gather feedback and write relevant epics, user testing from previous sprints
Planning - User stories written, acceptance criteria written, mockups validated, tech design and test cases
Active - Development Sprint
Typically, Product Management and Design will take a stab at accommodating a user story then bring in the rest of the team (PM, UX, DEV, QA) get's involved in fleshing out the UI and Acceptance Criteria.
In our first feature team meeting for a CSV upload feature PM presented the proposed solution. While is was a major improvement over what had existied before, one of the Devs had an elegant solution that worked even better.