Fluids acceleration on inclined plane

[haruspex]

Problem states that the closed box is allowed to slide down, not that it is sliding down the ramp. I interpret this to mean it eventually ends up moving horizontally.

I read it that it is sliding down the ramp. I see no suggestion that we are to consider a later stage in which it is moving horizontally.

At the curve the box will experience a dw/dt, a change in dy/dt and a change in dx/dt.
It could be that with different angles of incline, the differences in these values will cause the object to shift its position within the box.

As I posted before, there's a simple thought experiment. If the object has the same density as the water then you can replace by 'block' of water. There need be no physical boundary on this block, it is just a region of the water we choose to identify as a distinct object. Why should that move around within the body of water generally (other than rotate, maybe)?