I do believe it was Chestnut who pointed out a very good point while talking to me one day..... A LOT of ice is ABOVE the water. Some of it not even touching the water at all. If IT all melts then the water would in theory raise.
Ice takes up more space than when it was in liquid form because it expands as it freezes. So the water level would actually decrease due to global warming.
You missed the point, though. There is plenty of ice that isn't IN water. And expanding? That doesn't make sense. Cold makes things compress, heating up makes things expand. But again, all the ice that ISN'T IN THE WATER would then be IN THE WATER. That, would ADD to the water level.
Take your cup experiment, put water in it, an ice cube, and the set an ice cube on the top of the cup((not in the water)). Wait until all the ice melts. Did it raise or lower?
I'm just telling you what I've read and heard in documentaries on global warming.