Check YT. Brownell's has a couple of good videos on the proper method to measure barrels in all types of firearms.
For an AR (or any rifle), close the bolt, then run a dowel or cleaning rod into the barrel from the muzzle end until it makes contact with the face of the bolt.
Mark where the rod exits the barrel (tape, Sharpie, ...), and remove it. Measuring the rod gives the accurate, ATF-approved barrel length.
If HPD uses an external measurement and believes the barrel is too short, you should be able to explain the above procedure and how it's the ATF accepted method.