It was beginning to feel hopeless until I accidentally stumbled on a perfect solution: Kitchen Drawer Metal Trays!
The only caveat I'll add is that there is no standard size to the metal trays - some may be too shallow, or too wide or too narrow to work effectively. When you go out to buy one, carry a couple of paint tubes with you to test the tray. Most thrift stores sell these for a couple of dollars (or less!).
Share this freely with your artist friends.