Here's the brake that take's the Armalite 13.5" barrel to over 16" OAL. It's Armalite's competition brake, and measures out at 3.4" long. Camera angle doesn't show it, but that's the length...
So, with that said and shown, 14.5" .308 Win barrels are all over the place. Many, many manufacturers make them. That, without a doubt, is another solution to this, without another stamp... ADCO can cut and thread any AR barrel you want, as well - you can get a 16" barrel, send the mount with it, and tell them to make the combo 16.1" OAL, for a very reasonable price...