"First, as the oceans warm due to an increasing global temperature, seawater expands—taking up more space in the ocean basin and causing a rise in water level."
The ice melting is not the cause of seawater warming. Ice melt may indicate seawater warming, but the OP is correct that in itself it does not affect sea levels.
Actually, because sea ice has a different albedo than exposed sea water [0], sea ice melting is a significant cause of seawater warming (seawater warming is also, of course, a cause of sea ice melting; this is a classic positive feedback loop.)
Yes, the sea water absorbing more sunlight due to lack of reflecting ice could cause it to warm significantly. But this is indirectly caused by sea ice melting, and a more speculative connection between ice melt and water levels rising. Furthermore, I'd like to see hard numbers, since most of sea ice is under water and does not reflect sunlight.
"First, as the oceans warm due to an increasing global temperature, seawater expands—taking up more space in the ocean basin and causing a rise in water level."