This room is crazy. I currently have the absolute worst demo on C-net so am probably not the best person to give hints, but I did basically the same thing you described above. I used disoriented's trick above to do each branch, retreating back to the middle and letting tar growth envelop me before starting the next branch. This required leaving two tiles of tar hanging out of each side of the square, and I kept this rotationally symmetric (though I can't remember if that was actually necessary) In case it helps, I went with the East branch first, then the south, then the West, and the North last. I've attached an image of what things looked like the turn right before I stepped on the pressure plate.
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From there you can step on the plate and clear the remaining tar in the yellow doors letting you exit with the clone to take care of the rest of the room. I can post a (horribly unoptimized) demo if you want.
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Links to neat forum tools that I always have trouble finding:
Click here to view the secret text
[Last edited by Insoluble at 10-30-2017 11:51 PM]