Simple solution: Hire "Sammy the Shark."
Here's how the story goes:
About 5 or 6 years ago, I found a book entitled "Don't Eat the Teacher!" based on a shark going to school and "accidentally" eating everything in his path.
It's a funny little primary level book, but can be used at any elementary level.
What I bought was one of those long "picker upper" things (that happened to have a shark's head at the end)… and tell the kids "Uh oh…our room is pretty messy… looks like Sammy's coming out and you know what happens when he comes out!!!"
They all know that for every piece of paper, book, wrapper, etc. that Sammy picks up… they lose 5 minutes of the free time for the next day. After slowly walking around the room "pretending" to have Sammy eat some of these objects that are out of place, all of the students quickly gather to clean the ENTIRE room in a matter of minutes.
The catch is that they can't scream (we don't want to bother anyone, and that they have to put the items back in the correct place… not just shoved anywhere… and everyone has to help, because it's our room, not just my room.
I haven't cleaned my room in about 6 years.