The press release from Senator Hoeven mentioned a statement from Customs. The press release from Customs was posted on 23 April 2015. Here's a link: Temporary Exportation of Firearms

The good news in the statement:
U.S. Customs and Border Protection will continue to follow the long standing practice of issuing and certifying a Certificate of Registration (CBP Form 4457) to ensure that no traveler attempting to legally take their firearm out of the country experiences significant delays or incurs additional cost due to the implementation of a new regulation requiring an electronic filing.

The bad news in the statement:
Current export regulations issued by the Department of State require the traveler to file electronic export information (EEI) for temporary export of personally owned firearms via the Automated Export System (AES) prior to departure from the United States.

It appears that the Dept of Homeland Security/CPB does not have the authority to dismantle the new hurdles for "export" set up by two other cabinet-level departments: Dept of State and Dept of Commerce.

I suspect the snarl and tangle will get larger and messier before it gets undone.

--Bob