Belt Mountain makes great base pins. They make a couple of lengths, to address problems like this, and they also make an unusual one that has a set screw that fits into a small detent that you cut into the underside of the barrel. I didn't need that one but it looks very effective at keeping the base pin in exactly the right position. The additional advantage is that the pin doesn't roll when the gun is fired.
You'd want to send them all available information on your Dragoon along with a photo of your current base pin and its exact dimensions - length and diameter.