Crossing state lines with a MG, DD, SBR, or SBS is prohibited.
Now if you really want to cook your noodle, consider this situation. I have a registered MP5K SBR. When putting it inside an accessory such as the HK operational briefcase, it creates an AOW. The ATF's NFA division has informed me that this configuration requires a new form 1 and a new tax stamp to register this configuration as an AOW. At what point does it go from AOW to SBR? The AOW status is because its a gun that can fire while it is concealed and disguised as something else. So what state is it when the briefcase is opened and the gun is not concealed? You have to open it to reload.
So now you have an SBR mounted inside a briefcase that can be legally transported across state lines without prior permission. But while across state lines, you cannot take the gun out of the briefcase because then its no longer an AOW. Its back to a SBR. Are you even allowed to open the cause while you're across state lines?