Maybe six years ago a record breaking benchrest group was made by a smith, Jackie Schmidt, who chambered his barrel with the steady rest with truing cut method. His skill and obviously his record proves this method can work perfectly. Please note, he appears on the net chambering in the headstock with a 3 jaw set rue chuck. This is NOT what he did for this record breaker I referred to.
I just don't like using this method and it appears many don't either. Some use a pipe with cats on both ends. For those catching up, you can go as simple as 8 nuts welded onto a pipe, 4 at each end and corresponding set screws. The chuck grabs the pipe and the steady runs on the chamber end of the pipe. You can't measure where the muzzle is but, to me, normally it isn't important because I need two points to be true and the muzzle usually isn't one of them. I like to prebore so just behind the shoulder and a generous couple inches ahead of the throat are the two points. If a smith reams the entire chamber, the reamer will follow the existing bore hole so many dial in the chamber and ahead of the throat.
A reality check is Jackie's success with that method and his record. If we get silly with the method and theory and all the "how true can it be" talk, just remember Jackie's gun.
Back to the op. Just like my preference to avoid the steady with exterior truing cut, your call on live vs dead but my live is still good so I use it. Did you use a piloted 60` cutter to true the end of the bore for the live/dead to run on so you can true the exterior?