I've already commented on this before here. This will not work regardless of whether this is iron or lead or anything else. The fact that it was published in Nature does not mean it is true, always remember that.
A 108 kg ball of iron would have about 30 metres in diameter, which is not a lot, compared to Earth scales.
Here is why it will not work:
This is an interesting question that is maybe a little misguided. Instead of answering your question directly I'd like to draw your attention to some things that might get you to rethink your reasoning.
It turns out that what you're thinking of as the lower mantle (an assemblage of solid phases: mainly bridgmanite + ferropericlase + some other stuff) might ...
Perple_X (http://www.perplex.ethz.ch/) is software designed to do exactly that.
It has thermodynamic and mineral property databases for phases in interest. This is pretty much automation of method 3 given by the other answer.
In short, the way it works: you input your bulk composition, pressure, and temperature, and it spits out the phase relations.
A bit ...