Maybe it was made from sonotube?
Hank's case may have started out on TNG- in the screenshot from "Rascals" the case that young Picard is holding seems to have the later style integral strap, and in the shuttle screenshot the latch mechanism looks very similar to Hank's photos. Picard's case in "Liaisons" also has the integral strap. (it's hard to tell, but the two opening ones in "I, Borg" may also have the integral strap style - straps still seem to start from the top surface even though they're not under tension. Screencap is dark though)
How does the latch function? Is it a sliding mechanism? Or is that extended bar just there to support the other door without actually latching the doors together?