Nice looking gun, DLFL, from what we can see.....
Not to take anything away from Keith K., but you might consider going to:
http://www.parkergun.org/forums/and asking the fellows there of the Parker Guns Collectors Association who they might use. Many of them are located on the east coast and would probably suggest using someone much closer to you than risking the shipment of your damascus barrels all the way across country.
I speak from experience, having been involved in a matter where UPS bent a set of damascus barrels to a 45 degree angle with a forklift, thus rupturing them. They were insured for $5K, but UPS reneged paying the claim because they were "antique'/'irreplaceable" and were thus exempt from reimbursement in their minds. Took six months and a lawyer to get the money out of them, and you certainly don't need to contemplate that with your first Parker.
In the end, it's your choice.
All Best,
Bob