Cat, although I understand Archimedes Principle says that floating ice will not increase water level by melting, I am not understanding why you are bringing that up. The glaciers and ice sheets that create them on the Antarctic Continent are not floating. There are some ice shelves floating around the periphery of the continent, which come from glaciers flowing into the sea. The faster they flow into the sea, off of bedrock, the more ice displaces some sea water and raises the sea level, even before it melts. So, unless there is sufficient snow fall in Antarctica to balance the ice lost to glaciers sliding off the land into the sea, the movement of the glaciers into the sea does cause sea level to rise.
A more subtle effect is that the weight of the ice lost from the continent will allow the continent to float higher in the Earth's mantel rocks, with the ocean floors and distant continents sinking a little lower to compensate. So, on land local to the ice melt locations, sea level will then seem to get lower, while in other locations, sea level will seem to rise even more than would be expected from just the water level increase due to water volume increase.
I am, as I type this, sitting on a piece of land where "sea level" appears to be rising twice as fast as the average around the globe, because the land is also still sinking from the effects of the last ice age. This locale was not covered by glaciers, so it was squeezed upwards by the nearby land being pushed downward by the ice sheet. The land that was pushed down has been rising since the ice sheets melted about 15,000-to-20,000 years ago, and my property here has been and still is sinking back to where it would be at equilibrium in the mantel without any ice sheets in adjacent lands.