When the ice cube melts what was once ice will occupy the volume if water that was displaced by the floating ice cube to begin with. The part of the cube that was above the surface of the water will not cause an overflow. Another point is that an ice cube (or an iceberg) will float higher in saltwater than fresh water.
You obviously just don’t understand how global warming works.
The water piles up, so that the water level where the ice was is higher than the water that was there before.
Your grant funding is therefore denied.
Please study the article and re-apply when you learn how to reach the proper conclusions regardless of the fizzicks of the matter.