But in a molten core, won't hydrogen sulfide and methane bubble out from the center, leaving only iron and heavier elements and compounds in the super high pressure depths?
Very likely. But more studies would be needed. The best phase diagram for H2S and methane that I could find only went up to ~140 barr. Though there were some interesting papers on clathrates and methane in the kilo-barr range, but I'd not think those were interesting for deep earth experiments. The deep earth is ~3.3 mega-barr, for comparison.