I think you are trying to mix apples and oranges. lol (laughing out loud)
Push the envelope is trying to stuff so much in until it almost breaks. It is like stepping over the line. You go as far as possible and then you try to move the line a little further. Children are always stepping over the line or pushing the envelope during their learning curve.
It is like trying to go beyond what is currently possible into uncharted territory.
Thinking outside the box means to gather and entertain new information upon which you can base new and different ideas and thoughts. It is also pushing your thoughts into uncharted territory and thinking outside the box could cause you to push the envelope.
Pushing the right button is altogether a different concept. This has more to do with actions, reactions and provocations.