Don't know if that's a thermoset or thermoplastic but what about trying to heat the thingies again and see if the plastic will melt or at least soften to the point that you could squash away the gooey mess.
Amongst solvents I'd try acetone to start with. That strategy would be to "dissolve" it away instead of melting it. Won't work for thermosets though; they'll just swell. Others to try would be: MEK, MIBK, Toluene, Xylene, Methyl Acetate. Oftentimes a compatible cocktail might work better than any single solvent.
I've heard of a solvent called "Hexafluoroisopropanol" that will dissolve a lot of otherwise hard-to-dissolve polymers; but no first-hand experience with it. Might be a bit iffy to handle with its corrosive nature.
This plastic is incredibly hard and strong. It doesn't simply shatter like most would, if say...hit with a sledgehammer or something.
One trick is to cool it down and see if it becomes brittle; some do. If you have access to Liq. N2 it's worth a shot. Careful though. Don't want to make the medal shatter too.
However, I'm also a little puzzled how they made them stay put if it was all liquid.
Maybe they molded the bottom half and when it got solid enough placed the medal on it (in a sort of cavity) and then poured in the rest?