Is there no means through which such a large volume of surface water, perhaps delivered by comets, could be subsumed in to the mantle through tectonic processes?
Definitely. This was happening throughout most of Earth's history, it's happening now, and it will happen in the future.
Subduction occurring in subduction zones are the main mechanism (only mechanism?) of taking stuff from the surface and pushing it down deep into the mantle. Oceanic crust gets hydrated by reacting with the ocean water. Primary magmatic minerals such as pyroxene and olivine are altered into a variety of hydrous minerals: serpentine, amphibole, epidote, chlorite, talc, etc. Once this hydrated crust gets subducted most of the water is volatilised and gets lost to overlying mantle, and even flux-melting it so you end up having volcanoes. Here's a picture:
Recent research shows that not all water is lost. Some of it may actually survive the way down deep into the mantle. The identity of the carrier minerals and the exact conditions are still a field of active research and new discoveries are constantly being made. This would most likely form water-rich and water-poor regions in the mantle. The water content of the mantle will thus be quite heterogeneous, which raises the question of how representative was the ringwoodite discovery. After all, it's only one data point.
So to summarise it, yes. Water from the surface can end up in the mantle. This doesn't necessarily mean that this is what is happening, and it may be equally likely that the mantle water is indeed primordial.