Well first of all, for that technology to work (the one that interacts outside of the system), you'll need a second object. Your saying that the bottom half of the system will be the second object. The only problem with that, is that you physically have to manipulate the object in the real world to manipulate it in the digital world.
Not following you here. I think it would work, but I'm not an expert on the tech.
I'm not sure what you are talking about manipulating in the physical world.
You don't actually need a marked die to be your point of reference for you AR object. Besides you could always just use the bottom screen as a reference point.
Next you wanted to have the stylus be tracked by the camera so that you could interact with the object. This is feasible but I see a cord being attached to the stylus.
There are styluses that are a little smaller than the one for the DSiXL that that work on the same level I've described. Battery works fine and this one could be recharged just by putting it back in it's slot.
The popping out aspect, however, could never work in the holographic type of way you are talking about. As soon as you block your perspective with the stylus, either one or both eyes are not getting information to create the illusion of depth for your brain, and thus the illusion would cease to exist.
It's a great idea, but the combination of technologies that you have in your head (1+1 = 3), just isn't sophisticated enough right now.
I guess we'll just have to wait and see. It's not like your entire view will be blocked by the stylus, so I don't see how the entire effect will be null and void. But we obviously stand on 2 different sides of the line of what is possible, so we'll find out which side is right during E3.