FFLs can to that but many will not as it creates book keeping and legal issues for them. Once it is logged into inventory, the AFT and State regulations are applicable. To induce FFLs to do this, the fees would have to be pretty hefty and even then, FFLs might just refuse to do that. If the gun is not logged into inventory, the FFL may NOT do a NICS check.
So? The only way this can legally be done now without the FFL logging the shotgun in and out would be through MSP at the barracks ??