While the suction dredging operation is bound to work eventually, given that the blockage is holding up $400M of goods per hour (source: Lloyd's List), I would have thought they would have started hammering some big piles or ground anchors into the ground and using winches (and maybe rams?). I'm sure you must be able to get more force out of a bunch of big winches than a few tug props.
Given the cost involved, it doesn't really matter if they damage the ship - as long as it still floats, so they could weld attachment points if necessary.