From what I've seen of the Carbonite Freezing chamber in behind the scenes pics, It doesn't look as big as it did in the movie.
I would guess that room was not much more than 40 feet across. Yes it it still might be fudging a bit to get it in the vane, but not by as much as you think. Same goes for the falcon, you couldn't get those sets inside it, but it's not that far off, but it takes some fudging.