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.