What's wrong with shock cord? We use the fancy ones with plastic hooks, so they don't scratch. If we just hook the vertical drawers together, that usually is enough. For the drawer under the our bunk beds, I installed chrome bail strap hangers and run a Velcro strap through the handle and bail.
A marine hardware store, like West Marine, has a lot of hardware, straps, and Velcro to secure compartments and drawers.
Treat it like a home, use it like a boat. But only in very shallow water.