I am sat in my office in the tower right now and i have a nice comfy chair. This chair has a lever on the right hand side which when sat on can be pulled to lower the chair, and when unoccupied, can be pulled to make the chair raise. As i am only 5"8 i have the chair on full height. There is 12cm between fully extended and fully "sunk" (as such) which is round about 5 inches, do NATS not have chairs like these!?! If they did it would bring you down to a good 6"5 which im sure is the height of many ATCO's working for NATS. I feel sick at the thought of the situation that you are in, its utterly disgraceful, especially having been through the entire recruitment process.
Hope all works out for you