Incorporate full-extension or over-travel drawer slides with a simple “notch” in the wood strip attached to the slide that the case lip sits in. Case stays in place for pulling / pushing in and out, but lifts out easily when you want it to.
EDIT: I’ve been thinking about a smaller version of this for a while now. I want a small portable “things” without the hassle of having to empty out drawers. I have a bunch of these style cases - some are deep and red “ZAG” brand? Some are shallow and yellow "Stanley " I believe. Anyway, I want to be able to put 4-5 of the shallow ones in a holder or maybe two deeper ones and take them with me without having to carry them separately.
Overtravel drawer slides is where I am thinking of going. A case that has 5 sides, and then room for 5 of the shallow boxes or 2 of the deep boxes and one shallow. Then I can have my wire nuts, wire staples and cable related stuff( shallow), wall anchors and associated fasteners (shallow), and coated decking screws from 1.5" to 4.5" (the torx drive coated decking screws pretty much replaced all of my phillips drive coarse thread drywall screws a year or so ago.)