UPDATE -
I have done a little looking into it, and I’m switching the bedding from sawdust. I’m using fleece blankets as bedding now. As said, they will move the blankets around however they want, but at the same time as lining their cage, it gives them something extra to tear up. And if they choose not to shred it then you can just toss it in with your laundry. Also the blankets are much cheaper than traditional bedding, and safer for small animals such as rodents.