Okay, I spent a good portion of the morning on the phone with BATF and CBP and this is what I found out:
BATF had these two things to say:
Option 1. Go to the border with all the parts and the gun in a box with a letter from the gunsmith saying that you are shipping it to him for repair/reconstruction. Ship all the parts to him. Export is his problem.
Option 2. Have a BATF Form 6 Part I (as opposed to a Form 6 NIA) filled out by the gunsmith. Have him send the approved Form 6 Part I to you and then take the gun and all the parts to the border with the Form 6 in the box. Ship it to the gunsmith.
Needless to say, I was a bit skeptical on Option 1, so I called CBP to get their input. The CBP wasn't particulary impressed that BATF made that suggestion, and he agreed with me that the border guys would probably not react favourably to me arriving at the border with a gun in a box and no other paperwork other than a letter. He then said I could try taking it to a PreClearance desk (there's one at the airport in Vancouver) and tha I should consider filling in a TIB form (Temporary Importation under Bond) form, but then we looked through the notes and saw that it had restrictions listed in some document that we didn't bother to look up (we spent close to 40 minutes on the phone). He then said I should phone a Firearms Import Specialist in Washington State who would be more knowledgeable.
So another phone call, and the first question the guy asked was, "Why don't you just ship it FedEx? Why do you need to carry it to the border yourself." I was a bit stunned, as the option hadn't even occurred to me. He said all I had to do was have the gunsmith complete the Form 6 Part I and include that with the firearm when I take the package to FedEx. (He said I have to use FedEx, as UPS won't ship firearms.) This answered one of the questions I had about the Form 6 Part I, because it asks for a Broker. He said to just use FedEx as the broker, or if I really wanted to, I could shop around and find another broker instead, but why bother paying 2 different companies (shipper and broker) when I could pay 1 company instead.
He said export will be another issue.