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I wouldn't try anything yourself - the risks are huge and you could end up with no writing at all. The basic rule of dial cleaning is "if you don't mind ruining the dial, then have a go". I doubt you'll ever come across a replacement dial so, if it goes wrong...
If I were you, I wouldn't even try with Rodico, which is not a good thing to clean dials with anyway. As for dipping and removing the stained lacquer (if that's what it is), I sometimes do this when a customer insists and it makes me nervous so is not something you should try if you have no experience at all. If you decide to go ahead and dip it in something and it turns out well, then re-apply some lacquer to protect the dial finish.
Somewhere on the forum was a thread with a black dialled Connie (I think) that a dial specialist cleaned and re-lacquered. I don't remember the thread but it would be worth looking for. From the photo with the crystal on, it looks like some of the damage could be under the lacquer so, don't expect miracles.
Cheers, Chris
..........From the photo with the crystal on, it looks like some of the damage could be under the lacquer so, don't expect miracles.