Ok, to clear up some things here:
Water ice is less dense than liquid water. This is due to the molecular structure of water when it freezes - there is a lot of empty space (not air space, just empty space) between the molecules. They crystallize in a hexagonal lattice arrangement.
Link - near the bottom of the page is a drawing of water molecules when the water is solid.
Dry ice sinks in water. This is from personal experience with the stuff. Drop it in water, and it sinks to the bottom, and quickly becomes encrusted in frozen water, with only a small hole kept open by the constant outgassing of sublimating carbon dioxide.
Dry ice in a reservoir will only work if it's an open system, and even then, you'll want a good bit of specialized antifreeze, as carbon dioxide freezes at -78.5C (-109.3F). Otherwise, you're going to get ice. Putting dry ice into a closed system will likely cause something to burst, as the carbon dioxide gas is going to produce a lot of pressure.
Maybe consider a bigger radiator, or possibly some kind of peltier cooling arrangement, though even this could cause ice buildup with a sufficiently powerful peltier cooler. You also then need to worry about condensation throughout the entire system