Do an experiment... Add ice to a glass and add water to the rim. The ice should float a tad above the rim because it expands and the buoyancy changes.
However, the displacement remains the same. the water level will NOT rise. water is water.
As certain as I am that Catastophic Anthropogenic Global Warming(TM) is a complete fraud, your exposition of Archimedes' Principle is pointless. It is ice on land (Greenland and Antartica) whose melting would raise sea-levels. Also, in theory, as the oceans heat up, they expand in volume.
I argued that very thing with my bro-in-law and he's a doctor for cripes sake..............