Caro, I am a huge believer in tough love, but also heavy on the LOVE part. Now that your schedule has changed do you think that will help you to stay on top of her more? Do they use an agenda at her school?
Our schools all use an agenda. The kids are required to have them and all teachers write the work on the board and the first thing the kids do is copy it down in the agenda. The teachers will check it for those kids that need it per and agreement with the parents. If she threw out the list of back work then it sounds like you need to have it emailed home to you so that at least you have it. Yes she needs to learn to be independent, but she also is floundering and needs your guidance. If you give up now it would be the worst thing for her. Her brain isn't nearly done cooking and you have to keep helping it bake at the right temperature.
I like the folder idea if the 3 ring binder is just to much. Maybe just a file folder she can throw everything in and then you can go through with her at the end of the day. Even a pocket folder may be too much.
Also, this is a HUGE thing and would require a lot of perseverence on your part. You said that she was having free time because she told you that she had no homework. Obviously she has homework. And she has back work. If it were me I would tell my child that they will be doing homework no matter what. If they don't bring the work home from school then I will give them work to do. There are TONS of places on the internet where you can get math worksheets, writing assignments, you can have her do journal writing, you can find history and science questions for her to answer that relate to what she is doing in school etc.. I can send you tons of links if you would like.
Make it so she figures out that she would be MUCH better off just doing the homework that the teachers assign than the stuff that MOM is assigning. Mom stuff doesn't even need to be hard, just basic busy work. You really are trying to show her that you are not going to let her slide by and have free time if she just "forgets" her work. I would require up to 2 hours of mom work for every night she says that she has no work, until she is caught up with her work from school. I have a feeling that the work from school will not seem so bad in comparison. Taking away all privleges AND still requireing her to do work is a double whammy.
You may need to use Merle's suggestion to Tig also. Set a timer for 15 mintues and give her a reasonable goal to meet in that time. You need to do 6 math problems before the timer goes off, or write one paragraph etc.. That helps to break things down. With some kids it helps to fold the paper so they are only looking at the problems they are doing at that moment if possible. If there is a whole page of math, cover up all but one row with a piece of dark paper so her eye is only on the ones she is working on. Same with other subjects. It is kind of like putting blinders on a race horse.
Also, some kids just need to have you sitting with them. My youngest is like that. I just have to sit by her while she does her homework. Yes, there is a lot that I need to be doing, but this is my top priority so I will get a magazine or some work I need to do and sit right next to her to help keep her focused. I try to be gentle (some days are better than others!) and just point to the next problem or ask about the next sentence or word to refocus her when she is playing with her pencil or getting ready to jump out of her chair.
Okay that way too much thought for me before 9am and with no coffee and a shower. We are here with you to help.
This is exactly what I meant. Make it tough on her, but that doesn't mean that she doesn't have responsibility.
Can't believe it's almost vacation time for you! 
Yay for the pooch! 
with someone besides my kids and DH.
