Excavate sand around + weight from ship pancakes sand its sitting on, gradually = ship lowers back to floating depth
Also, I doubt the sand goes down very deep...this is a costal area, not rolling dunes. You're going to hit rock quickly.
which is not going to do much here. It seems the trouble with a lot of solutions - the tugs can probably tug with a force of something like 600 tons combined but the ship weights 220,000 tons which is like putting a force of 5kg on a 2 ton car which is stuck. Probably not going to budge it.
Really you want something which will shove it with a force maybe 10% of the weight, say 20,000 tons but there don't seem to be many of those lying around.
I wondered if they tied a cable from the ship to one of the other large ships nearby and fired up the main engines if that could do something?
That's when under speed. If these ships don't have the unidirectional port engines like cruise ships do for maneuvering in tight spots (and they may not, I don't know), in this situation they would likely use tugboats for turning. That's what they're for.
That doesn't necessarily make a diversion feasible, but I don't think whether it's feasible or not rests on whether these ships can turn. That's really not the problem as I see it.