Accurate and informative post.
I might ad, weapons going in either direction could be problematic. Do your homework if you want to cross with any weapons. Some are allowed for specific reasons such as competition shooting events and hunting.
US citizens are allowed to return to USA with weapons they departed with on Customs form 4457. Simple and quick to fill out before you leave the country.
Citizens of other countries may bring in weapons for specific reasons with authorized ATF form 6C or in case of hunting or shooting events, with proof that the subject will be actively participating in such events AND the weapons will be returning to country of origin.
Safe travels.
Lakeside