Might try the leaves then - if it doesn't work out, just remove them or augment with different materials.
Hope I explain this adequately... other people probably can explain it better.
True deep litter (which many deep litter folks don't actually use) is a composting system - the poop composts in place along with whatever else you have in the run and then you harvest the resulting compost for use in your garden.
The form of deep litter I use still breaks down the poop, but because I favor drainage over collecting usable compost I have a lot of wood chips in the mix (which don't break down very quickly) , so it does not make for ideal compost and I don't attempt to use it as such.
Deep bedding is just using a thick layer of bedding of your choice, ideally kept dry as it will not break down with the poop and because of that may need to be cleaned out from time to time.
I use deep bedding inside the coop and deep litter (not for compost) in the run.