I think you handled it well since it appears the outcome ended in a favorable result. But I would have done it differently since I don't care to trade my information for someone else's information; honestly they won't get mine. The fact that this person believes you need a special permit means whatever you present is likely not going to be acceptable.
However, if you block me in with your vehicle and you come up to my window in a long overcoat with your hands in your pockets and wearing a mask....I can't say exactly what I would do because it seems like it happened so fast to you but I'm glad you were able to record the interaction. People say this doesn't happen but relatively speaking, I think it's happens a whole lot more than it needs to.