MtG players are going to know what I'm talking about.
Check the top part of the boxes found in fat packs for that weird, almost unnecessary, cardboard insert. Slide it out.
That insert holds all of the most used double tiles, and a second one will fit the rest of the double and single tiles with just about an inch of wiggle room left over. The fit wide is perfect. Double tiles slide in with satisfaction and don't jostle around. Single tiles side to side, too. The second box is only slightly less snug, because there isn't enough tiles to fill it, but you can slide begging tokens in there to make it more tight.
I was looking for a better setup/breakdown/storage option than millions of zip-locks and now that I found these, I won't need to until I'm ready to totally pimp it out.