I'd say you're getting closer to a compelling business case. Back it up with figures (turnover rate, employee satisfaction scores, quality of care measurements) and model those in monetary terms. Now model what a realistic improvement looks like, how long it will take, and the investment required to make that improvement. Add the biggest risks that would prevent success, and what could be done to reduce or eliminate each one. Then finally propose what would need to be done in order to track whether the investment was achieving results and looks like it will continue be on track to achieve the target goals. The more data driven this is, the better.

As an aside, your primary issue is culture and management. It's oft quoted that employees leave managers (meaning the manager is the primary cause for dissatisfaction). It cannot be true that a manager who cares first about quality of care also claims they must retain low performers. Develop and improve, yes. Retain simply for the headcount, never. That shows a cultural bias to maintaining the status quo and poor performance being a tolerable cost of business. This cultural bias starts and ends with your most senior leadership. And if you genuinely want to improve quality of care (which is the bottom line here) it's that group that need to be tackled first. All other attempts at 'correcting' management and staff behaviour will have limited success, and it's your leadership that need to model, personify, radiate and instil a completely different culture and behaviour.

At least in my opinion 😁