I use my index and ring fingers to play the A from barr chord. I hyperextend my ring finger so that it does not mute the E string. It can be done, but it does not come easy or fast. I worked for years before that chord reliably and fully sounded that high E string. But as Dang ponted out, you don't need that E string to play a full major chord. Just keep playing that chord with the high E string muted, but work at bending that ring finger. Then one day, out of the blue, you will find you can hyperextend that last ring finger joint enough to play the full chord. Pursued with that approach, this ellusive chord form will just pop out one day, and surprise the hell out of you (at least that is what happened to me). Now I can reliably play the full chord.
When it comes to mastery...this is clearly a distance chord, not a sprint quicky. Just wanted to point out that it can be done with patient, perstistant, practice.
Captcha is a total pain in the........