Even as big as they are, high-rise tower cranes are still fulcrums and they should keep that in mind assembling or dismantling. If you pull all the pins on the way up, the first pin you pull moves the pivot point to the previous pin or anchor point
I know that in L.A. recently, the 3 small tower cranes we had attached to the structure, 9 stories up, needed 22,000#+ of counterweight to hold up 3,000# at 80' boom length and had a very specific order of installation and removal
In NOLA, they should've blasted the counterweights & booms loose before anything involving the towers (tower tops are the pivot points)