Rather than have trays for your kids to turn their work into, have them put their work in a paper drop folder. They check off their name on the list that it on the back of the envelope. Helps keep track of who has done each assignment and who hasn't.
This is where I had students turn in their work. I color-coded just about everything... almost all of the math work was done in yellow, all literacy in pink, etc. Their math folders were yellow, literacy pink. That way they knew where to put their completed work. Make-up work went in the bottom drawer.