×It doesn't matter how much the tar expands, so there's not really a time constraint. The only worry is killing the snakes.

From the lower 6 directions you can enter the orb-room. You'll get some tar-babies on the outside that can be used to kill the snakes (or if worst comes to worst, wait for the tar to fill the whole level :-P)

From N and NE, you can enter the tar-mother tar on a diagonal and again wait for the snakes to kill themselves.

From the NW, enter the room with the brain and two tar blobs, stand to the left of the door. Tar will expand before the snakes reach you, snakes should kill themselves in the doorway before two more spawnings.