This. If nothing else, shoving a stack of papers at someone tends to make them shut up and do it your way because they really don't want to get that involved in it.My advise for anyone flying with guns - print out the TSA policy and also print out the individual airlines policy. Have those with you at check in. And be flexible when things go wrong or not as planned.
I would never, ever let them tag the outside of the case. I would request a manager and explain the situation. Tagging the case is just asking for a stolen weapon.