Building a DIY home built Form 1 can used to be very easy when eForms were still up and before the darn fingerprint and passport photo requirements with trusts. My From 1 for my suppressor was approved in 45 days, it's the one I'm currently hunting with. Had it engraved with my Form 1 info so it's all legal and everything! lol. I built it in my garage with a pair of vice grips and a Dewalt hand drill. Those were the days.
As far as keeping the paperwork handy, I have a binder with copies of my stamps (form 1's and form 4's). I keep that binder in my truck or range bag. Keeping them on you or with the gun is fine, but when the number of forms goes above 10, it's kind of a pain in the butt. Even two shrunk down copies stuffed in a grip gets kinda hard. I've been stopped a few times while carrying NFA and only been asked once to 'prove that they're legally owned' (as he put it). I told him the forms were in a folder under my backseat, and that satisfied him. I had three sbr's and four suppressors in my possession that day, he thought the MP5 was pretty cool.
Anyways, I also don't care too much about keeping the copies on my phone. My phone is locked with a passcode and it will take a warrant to get into it. What am I trying to hide? I'm just protecting my rights for unauthorized search and seizure, fourth amendment and such. I've only had that happen one time in college, I won't get into that story.
Of all the times I've been stopped, either for traffic violations or for hunting license checks, showing respect and answering yes sir no sir, I think, has saved me hundreds of dollars. Getting snotty really doesn't help anyone and if they want to they can make life very difficult. Going back to the "you're not an ATF agent so I'm not showing you squat!", generally, a cop isn't going to haul you to jail unless, you know, you're doing something wrong or withholding information from him. I see a stop as an opportunity to show off some NFA items to a maybe curious officer and to answer any questions they have. To date, I haven't been stopped by an LEO who thought they knew it all. One Texas Highway Patrolman had to keep checking back in with his car because we stood on the side of the highway talking about guns for 45 minutes.