Quoted:
I don't think you will be able to get subsonic to cycle an AR. That said you need to get below transonic if you want to get rid of the sonic crack. If you are stuck on this run a 77 grain bullet as they will naturally have a lower velocity than the lightweight stuff, and run them at starting powder charges.
Trail boss is known for making safe subsonic loads in 308 and would probably work in 223. It sure won't cycle though. But that is not that big of a deal as it will be quieter that way.
"Below transonic" is subsonic. Period, dot.
Eliminating
all of the shocks on a bullet requires a speed well below supersonic speeds. The questions are whether it matters, is worth the trade off, or whether a suppressed rifle shooting 5.56X45 ammunition is the right tool for the problem where suppression of muzzle blast and supersonic crack is required.
Suppressed firearms are cool to fool with in any case.