If the ice melts that is under the water level, then the volume of the water will drop, severly

This is incorrect. Ice floats. The part that is under water provides buoyancy to support the part that is above water. As per Archimedes, "When a body is immersed in fluid, it experiences an upthrust equal to the mass of the fluid displaced". Sea ice already displaces liquid water in the sea. Melting sea ice will have absolutely no effect on sea level.