That brings up a question I've thought about a bit lately too... Lots of people seem nervous about being stopped and asked for paperwork. Can local LEO's even ask for that? Or only federal agents? My initial thought was federal, since locals have zero input over NFA stuff but that seems too easy.
Either way, just keep the digital file like you said and problem solved. I just can't see a local guy busting someone for not having paperwork. Most don't know the first thing about the paperwork OR process in general in my limited experience.