Are you looking to expand it left, right, the center, etc.? That'll sort of effect my opinion.
I'd look up a plastics distributor in your area. GE POlymer Shapes is mine, a division of GE of course, and they sell giant sheets (if you have a truck, it's something you're gonna need) for cheap. Enough you could do several floors up for it... Really nice.
For detail work you can hit up the local hobby shop that has a full evergreen display or plasti-struct display. Mine, unfortunately, is being persnickity and not putting a good display up, so I gotta drive a little ways. That's the detail work though.
The big sheets are what you need. Not too thin, but not too thick either or it'll be too thick to just score and snap off pieces you want. I have some here that I need to use a jigsaw to cut. Cool for projects where "thick armor" is a neat look, but a pain to work with compared to T-squares and Box cutter blades, ya know?
I'd say, I could see you doing a single stright rectangular "box" pieces that attaches to one END of the playset you have set up in that picture. If you could get a 3rd playset (mostly complete) and finish the guntowers at the top, you would really have a cool gunnery tower actually (there were I believe 3 in a row visible). The sorta rounded end would be cool looking I think, and then you'd have the other side (say the right side for arguments sake) as a complete, large "box" that makes up a structure on the Death Star's surface...
On the interior of the sets you have, I'd elmiminate at least one of the "chasm swing" levels by making it a solid floor, or opening it up as a chasm with no bridge... Wish I could draw this stuff for you DD, I have some cool mental images on it actually.
For the trash compactor I'd scrap much of what the set has and see if you can't actually build soemthing around the Screen Scene playset actually. The base is fantastic, you'd have to build the walls though.
Sounds like a lot of work what I'm suggesting, and I'm sure it would be, but it's just some thoughts I had. Not sure what kind of size you're wanting to go for with that beast.