[twizzel]

I bed on straw and do a cursory poo-pick when they're at the trough.  The earthen floor is, I think, much better than a concrete one.  Our shed is cleaned out as soon as the last lambs are turned out and bakes in the sun over the Summer.

Plus side of a concrete floor is you can disinfect easier though... pros and cons to all :-)

[bazzais]

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.