How to fix a black painted grille?

The stainless has already been covered, paint stripper should work well for that followed by a polish.

For the plastic inserts, I wouldn't want to blast them. The plastic will be degraded pretty easily. There are citrus based paint strippers though, which actually work well. I used them to remove paint from my traditional leather firefighting helmet, worked great without destroying the leather. Standard chemical strippers would probably melt the plastic. Before I used any kind of paint stripper though I would test it on a small section that isn't visible, or even on a broken piece from another grille to make sure it doesn't damage the plastic. And I would make sure to clean the parts thoroughly with soap and water afterward to completely remove any residue. Stuff that doesn't damage the plastic in the short term might still screw it up if left on there too long.

This is the stuff I used, not sure what it would be called in Australia, might have a different brand over there

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Shop CitriStrip 32 fl oz Paste Multi-Surface Paint Remover at Lowes.com