Jim, I saw the production twice on stage, in Boston and in New York, I was too young when the movie came out but own it now on Dvd.
AC doesn’t have the range for Caiaphas, I don’t think. He might have been able to pull off Pilate as that role has no physical demands.
While researching for this article I read that AC already recorded Herod’s Song some years back, but didn’t have to act. I listened to that recording, it lacked energy.