There are conflicting reports on this one, but I carry my Form with me both as a regular size, laminated copy in my range bag and as a reduced size laminated copy in the pistol grip storage compartment of my AR itself. Why?
Even if the BATFE doesn't require you to have the Form on your person, we are all too aware of the fact that police officers simply cannot know every aspect of every law on the books. Further, while some officers are enthusiasts just like you and I, there are still others who do not care much about guns and then others who simply do not like them at all. I carry my Form for the chance that an officer is present and inquires about the legality of my weapon.
I'd rather be able to show him "ze papers" on the spot than have him temporarily confiscate the item (or detain me) until I can obtain them from the safe deposit box.
Just makes life less complicated.