For the stone in the boat, when the stone is floating (in the boat) it displaces it’s weight of water, when it is at the bottom of the water it displaces its volume. It is more dense than water so it displaces more in the boat.
Interesting to see how other people deal with the same problem. The one in the OP is probably more generally applicable than mine.
My intuitions worked slightly differently.
The first one my intuition comes from the Falkirk Wheel (https://en.m.wikipedia.org/wiki/Falkirk_Wheel—see operations section)
For the stone in the boat, when the stone is floating (in the boat) it displaces it’s weight of water, when it is at the bottom of the water it displaces its volume. It is more dense than water so it displaces more in the boat.
Interesting to see how other people deal with the same problem. The one in the OP is probably more generally applicable than mine.