I did manage to figure the dang thing out shortly after posting. I especially like how Claythro's does this to me almost constantly. All part of a plot to drive me mad.
Hints for those who might follow:
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×1) Stand on the left side of the tar hallway, sword down, and allow the tar to grow towards the snake. Tar babies will keep the other side secure.
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×2) The tar must be controlled quite carefully. Set up the top gate as soon as the tar reaches, the bottom gate you'll need to wait till tar is concentrated down there. Speed is essential with both, watch the spawn counter.