
I love the Clean Sweep idea!
My brother went thru a messy/disorganized phase that my parents mostly did not interfere with, aside from making the rule that he had to keep his bedroom door closed so the rest of us didn't have to see the mess! When he couldn't find things, they would refuse to help and let him face the consequence whatever it was. Must have taken nerves of steel! I remember the wailing when something was "lost"! (My parents didn't interfere if I wanted to help him, so sometimes I'd help dig thru the piles or say, "Close your eyes and picture where you last saw it. What was near it?") Mom explained that due to her back problems she could not risk tripping over his stuff, so she would not be able to put away his laundry anymore; she would stack it in front of the door, and as long as he took it in there somewhere that was acceptable. Since he loved vacuuming, it was possible to get him to clean in there every so often by moving the heaps around.

:
The phase finally ended after about a year and a half, when he decided he wanted to rearrange his furniture and learned that his family would not help him until all the stuff was picked up off the floor and the furniture tops. One evening he was working on it when we heard an anguished yell: "There's CAT VOMIT on my carpet!" We did not respond. A moment later: "It's really old and dried up!" We did not respond. A moment later: "What am I supposed to DO?!" Dad yelled back: "Get a spoon and eat it!!" :LOL Shortly after, we found my brother in the living room consulting a book on stain removal. He was proud of removing the stain all by himself and told his friends the story as he showed off his rearranged and tidy room. He was about 9 at the time and has been relatively neat, clean, and organized ever since.

So it can work out...but sometimes the level of squalor necessary to inspire the turning over of a new leaf is higher than anyone else in the family can tolerate!!
Calgal, here's what I would do:
1. Don't tuck his papers into his backpack. That makes you responsible for their location. If you need a means of getting his stuff out of your way, have one general In Box and give him responsibility for getting things from there to where they need to go.
2. Don't help him look for his things at school. (You already know you don't want to do that!)
3. When he throws things and kicks doors because he's angry about losing stuff, don't even try to discuss his organizational habits at that time. Focus on listening to his feelings and stopping inappropriate behavior ("I hear that you are angry...but you may not kick the door.")
4. Wait until he's not in a crisis to suggest changes in habits.
5. Never, ever take it upon yourself to clean up his area without his participation! You will inevitably manage to throw away some useless-looking thing that is in fact his most precious possession

: and you will never hear the end of it!!
The above has been extremely useful to me in coping with my partner, who still needs Gentle Discipline in this area as an adult!