that barrel for the Glock you also have is an "assault weapon"

Points 1 and 2 are unclear. If you're referring to the threaded barrel for the Glock, the threaded barrel is not an AW. The format for determining what an AW is follows initial criteria (e.g. semiautomatic pistol which accepts a detachable magazine) plus at least one evil feature (e.g. threaded barrel). Obvious exceptions are firearms banned by name, semiautomatic rifles under 30" OAL, semiautomatic rifles with fixed magazines over 10 rounds, etc.

I think that this would probably violate the conversion part of the "parts" clause, because it would be used to convert an existing firearm into an AW.

I think that lowers you already own may get an exception because they're not firearms, rifles, or pistols. The parts you're importing can't by themselves be used to assemble an AW, nor can they be used to convert a firearm into an AW since they're missing integral parts to qualify as a firearm.