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You could try tumble polishing, well unpolishing it. Take it off the watch put it in a smallish plastic tub, pour in some cutting medium, play sand(?) screw the lid on, tape the lid on as well and then attach it to something that spins. Inside a bike wheel? Cable tie it to the drum in the tumble dryer and put it on the No heat setting? Tape it inside for a hole saw and run it in a drill?
I’ve not unpolished like this, but have cleaned up nuts and oddly shaped parts before. I did the drill one on it’s slowest setting for longer than you’d think.
It only gets the surface, and not into the mesh sadly so looks a bit weird