Its not a DIN size. It gets smaller both vertically and horizontally as it gets deeper meaning you would have to cut out all of the inside.
I'm not sure what you want to do here. Most screens that pop out of a single DIN location are also head units which would eliminate the need for your factory system. They also need plenty of space to pop out and your shifter may get in the way. Additionally, you would want the screen higher up for viewing pleasure.
The best solution would be to get a double-DIN unit and install it in the factory location. Then take apart the face of the factory unit and create a false-face-plate to stick over the screen, held in place with velcro possibly. You will need to glue all the buttons together making the factory unit useless but if it hides your $2000 investment...its worth-while. You can get a factory unit at a junk yard if you don't want to ruin yours.