You're on the right track.
What I did was take advantage of stunning to stun one sticky soulless with another, though I didn't have to stun the sworded soulless. For my solution, I had some turns left over and only needed a total of
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× 7 mirrors, including the one being pushed.
As for the positions of the soulless, the
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× sticky ones were diagonally adjacent and the sworded one was a knight's move away from the northernmost sticky one. The sworded one pushed the mirror onto the pressure plate.
Attached is a picture of the setup.