But hang on a few seconds - your cores are already a happening event, so what have you got to achieve? Stop it going anywhere ; stop any nuclear reactions ; minimise venting of volatiles ; cool it down. For stopping the nuclear reactions, you need either boron by the tonne or cadmium (and of the two, cadmium is a poisonous heavy metal and boron a bio-not-particularly-nasty ; easy choice) ; IIRC. For cooling it down and stopping it going anywhere, you really need thermal inertia ; dumping heat you can do by running it into a bed of sand or anything with a high thermal mass, as long as it contains enough (dispersed) boron to kill the reaction. Arranging your flow paths so the the core separates into multiple smaller, isolated units to increase the cooling surface - would that make clean up harder or easier. Reducing volatiles - I guess you need to choose your mineralogy.
Can you make cement with 30% by weight boron? Or cement with an aggregate of a high-melting boron mineral?
I'm sure this has been well discussed before, but I don't know the state of the art, and after an 8 hour meeting today, I'm going to the bar!