Hi, really cool what you guys are experimenting with here! I’m not familiar enough with the components and code at this point to be of any help, but I had an idea that I don’t think has been mentioned so far (sorry if I missed it!)
First I thought it would be cool to just have a piece of filament (or a wire cable, for strength) anchored to the front of the case on one side, and connect it to an extruder on the other side. So it essentially lays in a loop around the build plate and then, once the plate has cooled, winds in the filament/cable and “pulls” everything towards the front. Unfortunately there are lead screws that get in the way of that idea, particularly the rear one.
So that got me thinking about a similar setup, but in reverse, so it pushes the items off the bed. Picture this (hopefully my description will be enough lol):
Two extruders in both rear corners, towards the bottom. Each has a length (maybe 500mm) of flat spring steel around 10mm in height (like a metal ribbon) with one end anchored next to the extruder and the other end feeding through the teeth of the extruder.
When the print finishes, it lowers to the correct height and cools. Then both extruders feed the spring steel ribbons towards the build plate. The ribbons meet and push against each other, so as more is fed it starts to push towards the front of the plate and fill the enclosure…
I tried to do a quick graphical representation 
I hope it makes sense For some reason I can’t upload images or links to the forum 
so - imgurDOTcom/zfiyelm