Not completely unrelated: I worked at a shop that did tee-shirt quilts as custom orders, needless to say we disposed of the tee scraps fast as you can imagine the size of the pile from two quilts a week coming into the shop.
We gave them away three places:
1) a mechanics shop that specialized in restoring old cars, for parts cleaning and detail buffing
2) a salon, they loved old tees for waxing strips
3) the animal shelter, for both cage liners and bandages (they'd wash and use strong bleach first).
So, if you decide you can't use it all, there are some other non-land fill options