> Ice always accumulates in Antarctica, because whatever snow falls in the interior just sits there.

Not exactly. In most cases, the ice accumulates into glaciers and slowly flows towards the sea.

As you can see from this relief map: https://commons.wikimedia.org/wiki/Category:Topographic_maps... , Antarctica's interior is very mountinous and consistently a higher elevation than it's edges. Gravity forces the compacted ice downhill. As the ice on the mountains moves, so does all of the ice in it's way.