My suggestion would be to get an HK MR556 upper second hand, low round count.
Some guys are selling them with already cut down barrels, so you'd be ready to go. Or you get the 16" and have a competent gunsmith chop, thread, and crown it. The only real downside to the MR556 barrels are that they're not chrome lined or nitrided. They are cold hammer forged, though.
I chopped mine to 12.5" at work and used one of our industry partners that does our black nitride to treat the barrel. I'm happy with it, got what I wanted for a lot less than a real HK416 upper would cost.