I have a similar situation.. But my plastic box wouldn't keep things in place when it was new. I got a thin piece of foam rubber (about 1" thick) and cut it to fit in between the two halves of the case. Now when the case is closed, all of the sockets are held tightly in place byb the foam. It even took a "set" pretty fast and fits right into place like a glove. It's been working for about 30 years now, I haven't lost a single tool because of this. When finished wrenching, it is easy to look at the box and see what tools were not put away..
Perhaps this, couple with the strap idea may be your "fix".