If a glass of water was filled to the brim and had ice floating in it, with a significant amount of it sticking above the surface, gradually that ice would melt (assuming room temperature), and the extra liquid water would overflow.

I don’t understand what you’re saying. There’s a lot of ice above sea level, or otherwise removed from the ocean. Ice melts into water. More water in any container means a higher water level.

Global warming is wrong but not for this reason