I would argue that Luke was responsible for the Emperor’s downfall simply by his presence. You say his actions didn’t have any tangible effect on the outcome of the Battle of Endor, but think about what happens when you take him out of the equation. Without Luke, the Empire simply steamrolls over the Rebel fleet well before they have the chance to take out the shield. Because he wants to seduce Luke, though, the Emperor draws it out like a cat playing with a mouse. Palpatine knows he can wring some drama and torment for Luke out of the situation and that this will render him more vulnerable to corruption, so he keeps it going way longer than he has to. Luke nails it when he says “your overconfidence is your weakness”. He knows that if he can hold the Emperor’s attention, his friends will have a chance to succeed that they wouldn’t otherwise. It’s easy to overlook it with all the Vader drama, but really Luke is playing for time.

And as for “unintended coincidences”, isn’t that kind of the Force’s whole MO? Luke’s goals are fulfilled in ways no one could have foreseen because he chooses the light and doubles down when given the chance to turn away. That Vader himself turns and the Emperor is destroyed as a result is an affirmation of the whole saga’s cosmology.