I'm not sure why a Form 6 would be required to import a set of barrels. I've imported guns from Australia and from Germany years ago and the Frame requires approval, not the barrels.
Here's the instructions on the Form 6:
7. An unlicensed person may obtain a permit to import sporting type ammunition(excluding tracer or incendiary) and firearm parts (other than frames, receivers or actions) without engaging the services of a Federal firearms licensee, provided that the importation is for his personal use and not for resale.
Think the key word here is "May" not "Must". I think doing the form would be a way to prove ownership or it would be required if you were purchasing the barrels for commercial resale.
PS. I think the Forms leave a lot to interpretation for sure.
