This material is going to continue to sink until it hits something impermeable. At this point, groundwater contamination is the least of their worries, that's already a given, the problem should be recast as how to limit the spread of groundwater plumes. What they need to do is start building a geologic high-level waste repository on site and figure out how they can dump stuff into it, the most radioactive material first.
Maybe it's time to revisit Operation Plowshare (
http://en.wikipedia.org/wiki/Operation_Plowshare) and create and underground cavern that all of the "meltthrough" can drop into. That assumes that the geology of the site is conducive to such an effort. The more alluvium there is under the site, the deeper it will have to be.
There is a new effort at Chernobyl to repair the concrete cap with a containment building. Here is a video of their plan:
http://www.youtube.com/watch?v=jvEDVuGOJ6Y It should be noted that they still have a concrete bottom containment to work with, otherwise the Dneiper would be hopelessly contaminated by now.
Once they accept what has happened, the people in charge of Fukushima need to stabilize it with neutron absorbers and cover it over with concrete. That is the "up" part of the problem. The "down" part of the problem is what I mentioned earlier and depends on the geology of the area. It could be that there is nothing they can do but let another Oklo type reactor form (
http://en.wikipedia.org/wiki/Natural_nuclear_fission_reactor) which would continue to cook away for another few hundred thousand years.