The problem with that info is that it doesn't explain how to take the firearm out of the US again. Getting it to the gunsmith is relatively easy, you get the paperwork, take it in and UPS the gun to the gunsmith (you cannot use the US postal service as an individual to mail handguns) or physically walk into his shop and give it to him.
The question is how does the gunsmith get the gun back to you? Well, the best way is if he can do the work while you're there. If it's going to take a long time, you do have to use Form 6 Part 1 and then he sends it back to you... but he cannot send it outside the US without a DSP-5.
ATF knows nothing about export licensing, and I know of no US gunsmith who is AECA registered anyway.
I suppose the best way is to back into the US and have him send it to you at your hotel, or get a PO box and fetch it from there. Or you go and visit him and pick it up.