Think you will struggle with whatever you put down to be honest. I use wood pellets but found that my box walker would just spread them about and mix the mess in even when the base had settled. I would consider putting limited bedding in to just soak up the worst of it if possible although if the horse regularly lies down then rugs will become messy. Mine used to create a track around the stable he was so bad. He did it mainly approaching feed times and feeding ad lib hay helped to keep him a little more settled.
I would agree with minimal bedding on something like shavings with a view to removing everything daily. If your horse likes to lie down you could use a turnout rug instead of/on top of stable rugs to stop getting wee and poo staned rugs - can easily be hosed off then.
i was despairing with my box walker, but finally have a solution. She is in a big stable and has a regular route for her endless walking. So her bed is now much smaller and in a corner of the stable that she walks on less than the rest. The base is wood pellets (she wees for england) and that is left down until it squelches, the top is 2 or 3 slices of straw. Take poo out daily and any soiled straw, rake over base to level it and remove the squelchy bits, and more straw on top.
She always has something clean and soft to lie on , even though it isnt a huge bed , its big enough. Means the rest of the stable can just be swept. Far better than the disaster I used to be faced with every morning.
Aubiose on rubber mats, way better than shavings or straw. Much more stable and much more absorbent too so any mixing is of drier stuff anyway. And doesn't stick to horses manes, tails, rugs, your fleece.
Another one with a box walker . . . on straw. I really find that the deeper the bed (and the more established it is), the cleaner he is. I do a total muck out daily - lift the whole bed - but put the "dirty" (as in the stuff that I have left after I have removed all the poo and wet) straw on the bottom - at least 10 inches deep and then top up with clean. I find clean straw skitters about too much, but the more mature stuff makes a more stable bed that, once it's deep and heavy enough, hardly moves.
I have experimented with all sorts of bedding - shavings, bedmax, littlemax, flax, aubiose, etc. and, managed right, nothing is as effective or stable as straw.
I have a Sir Mix-a-lot who has been much better with a deep straw bed and no mats than any of the other options on mats. I'm not a big fan of straw on mats as it seems to get quite grotty and never dry.
Oh and I agree 100% with putting the dry straw on the bottom and digging the lot up daily.