I think more realistically you build a dedicated subsonic rifle and just shoot regular HV ammo out of your .223 can. You don't gain enough with the subs to make it worthwhile when you're limited to .22LR weight bullets. On the other hand taking your AR and putting a .338 BR upper on might make it worth doing. You've got a 300gr subsonic telephone pole coming out of the barrel and with good loading and workup with your rifle you can hit dogs out to 500yds with a heavy bullet and do it quietly. I know some guys think they should have subs for any gun they carry with a can but it makes more sense to carry a suppressed .22 pistol than to load .223 subsonic. That way you can take care of any close in stuff quietly and save a lot of time on loading a basic 22LR equivalent in your rifle.
This is just my opinion based on quite a few years of playing with subsonics and suppressors. I shoot a lot of full power .338LM, 6.5X47, 308 etc through cans and it works great. I only load subsonics for the .338BR and the 510 W though.
Frank