central river for automatic stabilization?

Ah yes! OK, I see it now.
I had been thinking that the accumulation of extra mass (the water) would pull the system even further out of whack, but the key is that as the CoM moves in ONE direction the water flows in the OTHER direction. The extra mass to one side pulls the CoM in it's own direction, in the process pulling the CoM through the geometric center. In a severe case, it might pull the CoM through the geometric center and a little beyond, but if that happens then water will flow the other way and pull it right back again. And since the water doesn't teleport, it flows at a finite speed, the whole effect is to dampen out the offset.

It takes some brain-wrapping, but I see it now. This is really quite brilliant and I'm amazed at how simple it is. This is almost certainly how it will be done, and all it'll take to keep people safe is an advisory to stay away from the river bank (or beach) for a while.