Anne Marie: I appreciate your step-by-step instructions. They are clear. With that in mind, I took David's advice and looked for tsuki ikkyo ura videos and I found this:
The nage in this clip moves straight back as my teacher and seniors want me to move, then enters and proceeds to do ikkyo ura. I don't feel safe when I practice this (as irimi nage) in class but I am told to not ask questions, just to do it. Okay.
I would not describe what he's doing as stepping straight back -- his orientation changes as he steps back so his torso is no longer in the path of the strike - it's particularly clear at 0:40 seconds, 0:50 seconds... He's moving to the side, but no more than he has to, and also part of the getting off the line of attack is accomplished just by hip rotation. If this is what you mean when you say 'stepping straight back' then that may be the source of much of the confusion people are having in this conversation.