But the universe can, at no point, be smaller than a string, contained within that string will be 1 or more dimensions with all the matter in, therefor the the big crunch wont necessarily increase the square footage cost of land on Manhattan Island.
We perceive the universe in 3 dimensions, with time being our fourth. String theory is consistent with a 10, 11, 16, or 32 dimension universe. Therefore the universe might well be compacting in other dimensions, whilst expanding in our own.
As you can see, i've not quite worked this bit out yet, but neither has Steven Hawkin either, so i'm excused.