What about, mornings doing non-exam aspects of your specialist subjects, ask the students what they'd like to learn about, life skills, relationships, social skills, mental wellbeing, enrichment areas... Then in the afternoons, PE / outdoor activities / games? It's not rocket science is it?
How are you timetabling this considering the rest of the school is still expected to operate as normal?
When am I planning these activities?
Perhaps if students were given a diet of a curriculum that isn't exam/assessment focused, they'd be more open to non assessed work. As it is, their motivation is for their grades.