Depends on how many things you'd want to link to a few counterweights. A few rfids on some objects and a couple of readers for positioning could do all the linking work you need.

Four linked ballast water tanks (Port Aft, Port Front, Starboard Aft, Starboard front) with pumps between them would probably be sufficient and would be much easier to place and maintain than other moving counterweights.

Yeah, your idea is much cooler than mine.

Some sort of Gyroscope might appeal to both your sensibilities?

Can a gyroscope in this situation prevent tipping, or does it merely slow it down? Honest question. Possibly even just slowing it down a lot would be sufficient since other forces could be brought into play to stabilize the boat.

I think you guys are putting way too many obstacles in the path. I live on a boat and I just moved a waterheater (~120 kilos) from port to starboard and it didn't make much of a difference on the waterline of the boat.

Yeah, I thought as much as well. It was said more in jest. I know a guy who put tonnes (3 or 4 I think) of slate tiling in his stern end and it only dropped it down half a foot or so in the water. Narrow boats usually have a flat bottom and weigh a huge amount, so they are pretty resillient... still, gyroscopes are interesting

Gyroscopes can only slow it down (considerably, sometimes), not prevent it. It could definitely make it easier to detect / rectify though, yes.