I was thinking a few lorry loads on the edge they are trying to pull, just to give it a kick briefly so the tugs can get that initial momentum going. More of a brief sudden kick/change to give it that edge.
With that I don't think with the whole damming of aspect would be any better than damming of and pumping water in. Also with that scale you run the risk when you breach the dam of causing what I'd call a saline tsuanmi which might not work well for the ships in it's path and may well cause another to get stuck.
So, more a form of quick kick to aid in getting the tugs an initial bite and a quick dislodge, however small, would only help and may well tip the balance.