I may be incorrect as I do not have a scientific background, but here is my opinion as to what appears to be going on here.
Water is a better conductor of heat than what air is, because of this any ice touching water will melt at a much faster rate than in air of the same temperature. The energy required to melt the ice cools down the water which in turn causes the colder water to fall to the bottom of the container the warmer water to stay near the surface. The entire surface area of the bottle will basically act as a heat-sink for the water where it is in contact with it, allowing the liquid to take in heat from the ambient air around the bottle.
This would mean that the water at the surface is warmer than the water at the bottom of the bottle, causing the ice at the surface to melt at a faster rate.
This does not directly explain the reason why the melted ice is above the surface, but when you realise that melting the ice is in effect removing mass from the solid block of ice, allowing it to float at a higher position than before, turning the whole system into a sort of moving melting 'converyor belt', melting ice at the surface of the water, moving up the previously melted spot to the point it is now out of the water and continuing the process which after some time would create the weird icy ridge hanging over the water demonstrated in the pictures & video.