FFL's are licensed federally. I'd hope the state doesn't possess the right to FFL's books.
Their playbook would probably be to force the FFLs to turn over transfer information. Don't forget, they also have FOID inquiries and the private transfers in their databases to work with. Never underestimate the ingenuity of a determined gun grabber, especially when the solutions are pretty obvious.
By means of their business licenses, be they state or municipal. For example, the primary and likely most numerou source: gun shops.