I've been in a similar situation at a previous place of work.
I ended up doing an internal audit against senior management commitment and I raised a non-conformity against the MD because insufficient human and financial resources had been dedicated to the food safety and quality management system. To be able to close out his non-conformance, the MD issued a set of priorities to all the department heads with targets for bringing down their own action points, with weekly progress meetings.
Addressing the issue in this way turned out to be pretty effective, because the MD took it personally that the non-conformance had been levied against him, and we made sure everyone in commercial positions understood that the consequences of failing to solve the problem would probably include loss of certification - so business continuity was at risk.
Another useful tactic is to report the number of outstanding non-conformities per department at each quality review meeting, so department managers have a sense of accountability for non-conformance close-out by their team members. You might find that the individuals responsible for carrying out actions don't always have a lot of decision-making authority over how they spend their time, but the department managers do... So building CAPA into departmental KPIs can be quite helpful.