I so feel your pain!!!!! I have three kids, only two in school but started to see how difficult it was going to be to keep up with homework, papers, cleaning, raising, LIFE!
I went a very simple route to keep track of everything. I did what you did and put hooks and a big basket right by the garage door where we go in and out every day. The first thing they do is hang their coats and backpacks on the hooks, and put their shoes in the basket. I have one son that likes to get on homework right away and one that waits until after dinner to do it. This of course creates a situation where I am getting bombarded with papers at different times so I created a homework/school drawer in the kitchen for each kid.
I do not have papers separated or organized in the drawers I just put them in there. I have also trained my kids to keep the homework they need help with or need me to check for them in a pile (all together) so I can easily sit down and go through it. Basically when they are ready to do homework, they bring their bag upstairs, sit down and do it, then leave me a pile of check stuff.
I typically do not have time right when they need to go through everything as I am doing dinner or bathing a baby or whatever for the night. by the time I get them in baths I sit down and hit the homework piles, it takes me about 30 minutes to check everything and then make sure they did all of their homework. Notice, I have not even looked in their school drawer yet.
Once I get them all to bed, and if I am not too tired, I will look through their drawers. This is when I can sign what I need to sign, read through what I need to read and add to the calendar any important dates. I am very much a morning person, so a lot of time I get up an hour and a half before they all get up so I can get showered and ready for the day and go through the homework drawers.
The one thing I cannot do is let he drawers go for even a day. I touch them every day so I don't miss anything. I also do not put too much energy into them so I don't lose a ton of time every day analyzing everything. One last thing I do is be sure to THROW AWAY!! I try very hard not to get too attached to anything and only keep what is REALLY important, as soon as it is outdated, I dump it. Otherwise the homework drawer will not be able to close by the end of the year.
Good luck!