I concur! In addition to that, icebergs also probably don't have a unified mass just based on the proportions. Some parts of the iceberg will be snow, others will be very tightly packed snow while others will be just ice, also with different densities.

So the iceberg could very likely float like that when taking into considering 3d space + the random distribution of mass that is different in different parts of the iceberg.

This kind of drawing matches early year mechanical engineering courses.

The generalizations are to add density distributions and the 3rd dimension.

The math generalizes just fine for picking points that are stable. The motion on how it gets there relies on the full Navier Stokes vs the simplifications, so I wouldn't trust that you've actually gotten to the right stability point

One way to avoid this might be to create an internal 3D model by rotating the drawing about the y-axis.

It's just potential energy minimization. A tall thin iceberg will float on its size in 2D or 3D.

That’s assuming the 2D representation is representative of near uniform density. In 2D an I-beam and and a solid beam look identical, but they don’t represent the same amount of mass for potential energy minimization.

Play with 3D shapes and you could get identical 2D cross sections to float in arbitrary orientations.

You can but only under very arbitrary situations that aren't common in real life. And if you're assuming it's not hollow and has constant density, then I doubt there's any way to make such an iceberg except if you look at it from one specific angle: looking from the side should give it away. Yet nearly every image of an iceberg seems to show them in that way.

That’s a different question. In practice floating icebergs are often at a local minima not the global minima. They can be at very unstable orientations in calm seas. The constant melting process promotes instability.