I think you could take one of two approaches. First, get clear medium sized bins and put in those- Costco or Sams may have them in bulk at a good cost. Or you could take fabric (folded like it comes off bolt) and using the ruler method fold it so it ends up being approximately
7" X 11" roughly. 44"/2= 22 then folded in half makes it 11" deep. Then put on your shelves by color and since you have LOTS you could do two deep on your shelf. When you stack up fabric that way by color you quickly SEE pieces that need to be together in a quilt. For small pieces or scraps clear shoe boxes work really well - the IRIS brand seems to hold the most- no rounded corners on those. There is just one problem with all of this organizational stuff - it is like laundry - it just keeps needing to be done over and over again. Good Luck!