There are preservation systems used by libraries that will continuously do what you're describing: https://www.archivematica.org/en/
Give them more than a few weeks to get comfortable with you and the company culture.
Give concrete examples of things that have improved due to employee feedback.
It's hard to offer better advice through a HN post but easy to observe in person. Perhaps you can hire an external consultant to help or ask a mentor or advisor to fill this role by spending a few days in your office.