yes, I agree it is very unlikely.
What I would do is try and construct a way to not need to rotate the ballistas (since by definition that can not work outside of a 1 in a million type shot).
I would do something like set up a large square.  Each corner of the square would have 250 ballistas pointed at another corner of the square such that all 4 corners were covered by 250 ballistas.  The 250 ballistas at each corner would all be lined up to spread their shots both in height and width fir maximum coverage.     
The hope being that when the Dragon swoops to flame one of the corners of the squares, the corner that is covering it launches all 250 at once.
This only has a chance if the Dragon's don't have much range on their fire breath and have to come relatively close to the ballistas to flame them.
 
