According to the story as you posted it and absent any facts left out, he had no grounds to search the vehicle without consent. It would be reasonable to have you exit the car and move away from it and secure any weapons on your person.
He conducted a search of your vehicle and a seizure of you and your property extending beyond the scope of the traffic stop in order to check the serial numbers of your guns. For this to be legal, he would have to be able to show that guns transported in vehicles are more often stolen than not. This would give him probable cause to believe that the guns you are transporting are stolen. I doubt that he could prove that to be true though, unless Garland is rougher than I remember
Otherwise he would need to be able to "articulate" the "facts" that gave him probable cause to believe you were transporting illegal guns. The fact that you were transporting guns was not enough (unless that was in itself, illegal).
Bear in mind when I use the term "legal" I am referring to Constitutional law. There are plenty of illegal state laws out there.