I found that, using MaxMSP, it is possible to 'hack' the Ableton Push 2 Display into forcing it to show custom content, instead of it's usual parametric information. You'll have to manually put the Push in to 'User Mode', and then basically run the patch below in order for MaxMSP to take it over from there. The patch uses David Butler's imp.push package, and expects a Syphon/Spout path in order to receive external video from. This video source could be sent directly from your favorite VJ or Mapping software.

Here, I use VDMX's Syphon output for example. I'm previewing 4 layers (+ 4 mask layers), 2 logo overlays, 2 selected colors (both white) and my main output (black for now).