Can't finish quest "Speaking With Silence"

I'm having a problem with the quest Speaking With Silence.

The problem I'm having is not with the door but with the cut scene where the player is shot with an arrow - it won't start. Mercer has opened the door and we are both standing in the final room, but nothing happens.

I've tried loading a save from before entering the dungeon, but it still doesn't work.

I'm playing on Xbox 360.

According to this bug list for Speaking with Silence, a proposed solution is the following:

This can be fixed by entering into the hall in first person after reloading a previous save

Other suggested fixes, courtesy of this post, are:

Waiting 24 hours, before entering the room and after

and

Restarting the quest from a save right before entering Snow Veil Sanctum, and a save before you have the quest in your journal.

Every other fix that I have come across involves using console commands to fix the situation, unfortunately.