You wont get the advantage of the 77g out of the short barrel; shortest I'd go is 16 with 77g.
Plus remember, M193 needs to be at 1700fps at a minimum on impact for it to reliably fragment. 77g design is different and relies more on the yaw/tumble/hydro static wound channel as far as terminal ballistics.
That's why I'm saying either run 5.56 in a shorter gun because 90% of engagements are at less than 200 yards (you wont be under 1700fps until I think somewhere around 300+ with an 11.5) and CQB with a 20" A2 just plain sucks. The extra length just isn't worth it to me. Or, if you're going to need some distance yet want to not paint yourself in the corner with a bolt gun or a heavier SASS, the 16" Mk12ModH is truly a do it all gun with the 77g.
Otherwise, if you think you're going to be shooting some decent distances consistently, you need something completely different than the 5.56.