I know this is an old question, but another option that you might consider is sawing off the existing rings with a jeweler's saw, smoothing the side, and then setting the entire stone with the existing electroplated bezel into a new setting. @Chris Johns is right...you can't resolder the piece because of the potential for damage to the stone.
You can sometimes use certain stones safely with precious metal clay which is going to be finished in a kiln, but the fractures inherent to a geode would not fare well. So you really need some sort of cold setting option, which led me to thinking about bezel setting.
If you create a custom bezel setting for this piece, you could encapsulate the entire old setting within the new bezel. You could create a bezel in the traditional manner, with silver plate, bezel wire and a ring, and solder all of the pieces together, then insert the stone and old bezel into the new bezel. You could also make a new bezel out of precious metal clay (just make sure to account for the shrinkage that is inherent with PMC).
Either of these methods allow you to use high heat for the metal itself, without any impact on the stone. You probably won't be able to use the burnishing process with this piece because the stone's face is so rough, but you could use an adhesive like E-2000 to attach it into the new bezel.