77-grain bullets are great (I'm assuming you are talking about Match King/Mk.262 here), but like I said, that makes your rifle's wounding capability dependent on the availability of a comparatively rare type of ammunition. If all that's available is the normal ball stuff, you are out of luck, because that stuff will not perform well from a short barrel. Earlier, one of your reasons for choosing an AR was that it uses .223, a popular round. But the popularity of .223 in general doesn't do you much good if your rifle only has good terminal ballistics when used with a particular type of .223 ammunition, and that particular type is expensive and uncommon.

You could also get a .308 AR for much less than you'd be spending on this Addax 10.5" AR setup you've described. According to the Addax website, their 10.5" upper is $1265 by itself. Add in $200 for the SBR tax stamp, plus $300 or so for a lower, plus $400 or so for this Aimpoint you want to put on it, and you are talking about a $2000+ rifle. You can easily get a very good .308 AR for under $1500. Or, even better, a good FAL for around $1000 or less. Or just a 20" barrel AR, which would have good terminal ballistics out to 200 yards even when used with normal ball ammo. Why is an ultra-compact carbine desirable? Like I said, we're not talking about riding around Baghdad in a Chevy Suburban bodyguarding some VIP.