I was planning on leaving a few inches to spare at the top anyway, but I'm a little concerned because the slab has cuts in it (to guide cracks) and one of them is right in the middle of the room I was planning.
ChunkyMonkey, you're thinking in the right direction. I considered steel, but in my limited research, it seemed that concrete was easier to work with and had a better strength to cost relationship. I could be convinced otherwise... I haven't done enough research yet.