> We still know very little about the deepest parts of our ocean and until we can more easily explore them I don’t see how you could say with any certainty there’s no ice down there

We've been to the deepest point of the Ocean. We know what the pressure is there.

We also know what pressures are required to form the kinds of Ice you are discussing because we have made them in a lab.

The pressure difference between the two nearly 10 times greater than the pressure difference between the bottom of the ocean and the vaccum of space. It's not even close.

Edit: to help more with scale, the pressure under question (1 GPa) is roughly the pressure range we expect for the Mohorovičić discontinuity - the boundary between the Earth's crust and mantle. If Ocean water could come up with that kind of pressure, there wouldn't be an ocean floor - because the pressure would push it into the mantle.