The only way that ice can be below sea level is if it's pushed down by something. In this case, the ice below sea level is pushed down by ice on top of it. (Which is why an iceberg is 90% below water and 10% above water.)
> "Since water uses more volume as ice than as a liquid, the amount of liquid held in the bowl, should be more than the amount of ice it previously had, before melting."
I think the mistake that you're making is that you think there are icebergs which are below the surface of the water, but they are less dense than the water. Of course, this can't happen. It's like having a helium-filled balloon that falls to the floor, even though helium is less dense than the surrounding atmosphere.
You have to take into account the fact that 10% is above water to begin with. As it turns out, those two things cancel out - i.e. the volume used up by ice which is below sea-level is exactly the volume of water that the a melted iceberg will use-up (after it's melted). This is the same principle used in ship-building: the weight of water which is displaced by a ship is equal to the weight of a ship. (
http://en.wikipedia.org/wiki/D... ) Similarly, the weight of water which is displaced by an iceberg is equal to the weight of an iceberg.
You can test this easily enough with a glass of water. Fill the glass with ice. Now, fill the glass to the brim with water. Some ice will stick out above the top of the glass (because ice is slightly lighter than water, so part of it will float above the surface of the water). Wait for it to melt. The water level will remain constant (it won't go down and it won't overflow).
> "Seems to me that the net result of this should be lower global sea level..."
No. That would only be true if you ignore the fact that some of the ice is located above sea-level. When you calculate all of it together, you'll find that ice in the water won't cause a sea-level change when it melts. (And the sea-level change that global warming people worry about is caused by ice melting which is currently located on top of land.)