I'm getting no indication that this room has a fun solution. As best I can guess the solution is to wake up an eye and use the goblin to get to the south of it.
I've tried something along the lines of
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×using the NW eye to block the eastern eye and can get my sword pointing north with the awake eye blocked on the sword, but can't deal with the goblin.
Seems like there's some specific setup that works for this and anything else won't work.
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