Dragonfire will melt practically any material, but much like regular magma it needs time to melt items. If the dragon is only breathing on live goblins, then when they all die it'll stop burning the metal.
Regular fire will only ignite flammable items, namely clothing, wood, and coal. If it does any damage to metal and stone, then it's so little it's never noticed. You could use alternative fuel, like wooden goblets in a stockpile that forbids bins, so they're spread thinly, but I'm not 100% sure that fire spreads to adjacent items - I know it spreads to adjacent tiles, like grass, but unsure on loose items...
Since you have a volcano, I'd suggest a brief wash. If you make your kill zone like this:
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You can have solid pillars surrounded by floor grates (iron, magma safe!) and the upper level covered in the same pattern, except using hatches. Fill the hatch-level with magma, when they open it'll give a very quick wash of magma onto the floor beneath, which is instantly drained through the grates, to be recycled for more burning, discarded, or pulled into a nice magma mist generator or something.
Granted, that's 3 iron for every tile - the grate, the hatch, and the mechanism in the hatch - but what's stockpiles of metals for if not extravagant death chambers?
NINJA: Loam, why are you against huge, convoluted systems? Why do you love the elves? Just tell us, we can provide help... We care about you man and we don't want to see you go that route.