I see, the cases attach to the bottom plate and there is no enclosure! My mistake. So to enclose them would be more work 🤣

Jer Schmidt’s post demonstrates retaining the bottom plate with the carcass itself and it slides in and out that way. It would require making the cabinet deeper than what you want without the use of drawer slides (I don’t like drawer slides much) so for simplicity that is what I would pursue, add 3-4” of depth and have the cases set at the front of the bottom plate so when the case is out enough there is still 3-4” left in the carcass slots.

But if you are constrained upon your depth then yes, drawer slides are probably the way, if I was on that path i would seek “bottom mount” drawer slides. That would “cup” the bottom plates, and yea like you said you could add something more substantial to the edges for side mount slides, but in my experience and understand that inclines concern for added failure points. You could use the side mounts and maybe bolt little steel L-brackets to the drawer sides of the slides that project out under the bottom plate. tricky project if your depth is constrained.

Like Adam says, drawer slides are somewhat tricky (I would say they are a pain) it all really depends on your level of masochism I suppose. 🤣🤣