This thread seems like a good place to ask this. Sorry OP, will piggyback your thread for just a bit. My answer to the thread myself is originals stay in the safe, I make photocopies, cut them into wallet size and laminate them. I bought a luggage tag that I attach to my range bag so that's where they go.
Now on to my piggyback question...I overheard a small debate about what someone previously said that they put their papers in the pistol case. So one guy was telling another guy that he shouldn't keep papers in box because if ever pulled over by LEO, and asked to produce registration, he would be in trouble for unlocking case on the side of the road to produce said papers. Other guy defended it by saying he would be instructed so it's okay, but other dude said it would be a "trap" and not all LEO's know the regs as well so he may get lucky but why chance it. Your thoughts...and again sorry OP for hi-jacking.