I really like these ideas about making a 'stronger Vader' for ANH (ROTJ Vader needs help too imho).
About the current discussion, I think it works quite well removing the "Terminate her, immediately!" line.
As it is in that clip though, the only thing that feels off to me is the long awkward silence of nothingness now after Vader says "I told you she would she would never consciously betray the Rebellion". It worked before because then Tarkin would say his line; since he doesn't now, the scene needs to feel like it's "moving along" quicker.
My suggestion, either:
A) Have Vader's line pushed forward a few frames so that it feels like we aren't waiting for too long before switching to Tarkin's annoyed face.
B) Have Tarkin's movements moved forward a few frames so that he is already standing still once Vader finishes his line, then we immediately switch to his annoyed face. By doing this, the scene will also be shaved a few frames. This would require more special editing skills.
C) Or, just thought of this, insert a brief pause between Vaders's line so that now he says it as two sentences, instead of as one. Like this, "I told you. She would never consciously betray the Rebellion." Then by the time he finishes his line, we're now at the point when the camera switches to Tarkin's face.