Not a Parker but this is my early LC Smith Syracuse extra heavy Quality 3 10 gauge with 32" barrels that had heavy pitting near the breach. The work was performed by Brad Balchelder who used laser to weld under magnification. Call him and I'm sure he will explain
how he did it since I am not sure exactly how he did it. In any case, to do this on Damascus barrels is amazing. I'm sure he can help you with fluid steel barrels too.