How can I stop my bunnies weeing and pooing in their bedding area?

I have two 11 week old Does (from the same litter). I have a two storey hutch that has a ramp from top to bottom. The top level is 1/3 bedding area and 2/3 open with wire mesh. My problem is that the majority of all wees and poos end up being done in this bedding area. I put newspaper down - then a few wood shavings and top with plenty straw and a little hay. Every morning I lift up the straw and the paper is sodden and there are loads of droppings. I do have a little tray (which looks a bit like a dustpan). If I put this in the bedding area it will make it very cramped for two bunnies. Does anyone have any idea of what I should do as this is going to cost of fortune changing their bedding every day. Also, as winter approaches I will want to bring them in to run around a bit but not if they are not fully potty trained. Any ideas.