If you can't find a builder who also does bluing I suggest looking for one of the companies that does just metal finishing including bluing. Be sure to check on your description and what they can deliver to be assured of getting the 'depth' your looking for. You want a company or individual that understands real firearms bluing, not just changing the color of the barrel.
It is possible that you will need to blue all of the metal work to get everything to match.