Photoshop :: Semi-3D 'Toy Theatre' Effect

I've seen it used quite a bit on TV recently, particularly in history documentaries, where they've taken a picture (often an old image such as the bayeaux tapestry or an old painting) and sort of 'disassembled' it and added effects, to give a front-to-back semi-3D look, almost as though the figures and elements in the picture were flats in those old-fashioned toy theatres, or maybe a pop-up book.

I've had some experiments in achieving the look in PS, using things like drop-shadows, and slightly blurring foreground and background elements, but it never quite looks right; often there's some impression of depth but the 'space' isn't quite there.