I understand your point a little better now. In your drawing yes, 24 volts would go through A2 and B2, through the two e-stop contacts and go back into A3 and B3. That part sounds correct.
I think you might still be confused about A4 and B4. These are outputs from the safety controller that should only be energized when the e-stop is in a safe position. They control the optoisolators, but they also control two relays to energize the main power circuit. These branch up right after the names. So even if you did have the e-stops bypassed, your connections would not have driven the relays or optoisolators. Referencing the second drawing, A3 would not go to A4. They would both, theoretically, have 24V potential.
You are correct about A5, A6, B5, and B6 being tied together internally to the systems ground, so the jumpers on these terminals are a little redundant and made it kind of confusing to look at.