If this had happened to me I would be contacting his superiors to find out what they have against gun owners in the woods. Someone had to train or tell him to ask for ATF forms. It sounds like this guy is a loose cannon especially when he is looking for something to charge you with when he can't get you for shooting in the woods. He has "corrupt cop" written all over him.
Federal law does not say that you have to keep the forms with you, it does say that the forms have to be shown to the BATFE when they demand to see them.
Lark is free!