Do you have an inverter yet? If so check out this area to see if it is close to fitting. If not I would look elsewhere. You should be able to otherwise trim much of this area away without problems. If you remove the console it will be easier but it is not required. The colored pieces come off the black inner core easily. I am not sure how it mounts to the dash but it looks like you removed a couple bolts? Long silver ones? I had a loose one laying in my console that I couldn't tell where it when and I bet that was where it went.
If you look in the drink holder slot you will see a black bracket. This bracket goes under the mounting bolts for the front seats. So you have to unbolt the front seats to pull the console out but it should come out relatively easy. The wire to disconnect is below the drink holder area.
The black piece in this picture is actually riveted to the rest of the core so you can't just remove it. If your inverter is close to fitting you could hollow out most of the area you show in this picture and it would be open to the dash in the rear. If you look at the rear of your console where you took your pictures and you compare that to this front section you can see where you have room and where you don't.
But again, as I said, if your inverter is close to fitting into this spot you could easily put it in there. Otherwise I wouldn't bother digging further. It could be modified to add a double din radio easily. I am mounting a 10.1" flat screen in mine. It is at a shop being glassed now. I don't know how it will look yet because I didn't talk to the guy actually doing it but the black piece and the surrounding piece I suspect will be glassed into one piece with my monitor inside it. If you were to decide you wanted to put a screen in there I will be posting pictures when I get it back.