Put new bedding on the old - it makes a nice bed for them, warm and insulated (mind you I dont know how big your pen is or what size or anything for your 4 - I only muck out when winter is over. (I lie sometimes it stays in there all year)
It takes a bit of time to build a good 'bed' but once its there - imo it help the 'drainage' too of wee.
You can always light dust with hydrated lime to get ammonia down and for feet and disinfect. (not when they are in there)
As for disposing of it I suggest may fencing off a tiny corner of the land they are on for the other 8 months with a few pallets and lob it in there it will decrease in volume and and make it easier to handle or transport.