Reducing DNA rates — what has actually worked?

Our DNA rate is 9.2%, which is above average and costing us roughly 40 GP appointments per week. We've tried SMS reminders (marginal improvement), calling the day before (too staff-intensive to scale), and online cancellation links (patients don't use them). I've read about 'appointment fees' but obviously we can't charge. Has anyone cracked this in a sustainable way that doesn't just transfer the workload burden to reception?