My son would never clean up his room... if I told him to do it, he would shove everything in the closet or under the bed... sooooooooooooo, one day I told him if the room wasn't clean by a certain day, I would clean it. I believe this scenario happened a few times until one day when I was cleaning it, I accidently threw out his magic tricks. When he discovered this, he also discovered it was garbage day and they were gone. After that, his room remained clean and spotless until he moved out. He was about your daughter's age when this happened.
One thing that I did to help it along was his choice of sleeping... he had a sofabed in his room, a coffee table, and a table that served as a TV stand and storage. This allowed him to have his own "living room" for his friends to visit.
On the other hand, my daughter was extremely messy and nothing worked but today she is the perfect housekeeper... but then so is my son.
So, in hindsight, I would probably try the "you cleaning her room" after giving her so much time. I would preface it with if something is thrown away accidently, it will not be my fault... and then go for it. Who knows... it might work after one or two times. Good luck!