I originally did this hold in the Architect's Edition, so I sympathize with the problem. I would get involved with killing the tar babies in front of me, I would lose count of the number of turns taken and, all of a sudden, the tar mother would spawn and I would get killed by a tar baby coming in from the side. Also, when I did this level, there were no destroyed driveways in my neighborhood, so I sent my kid brother out to pulverize one of the neighbor's driveways. Unfortunately, he took way too long to be of any use, so I had to figure it out without a counter.
Since you are using the SW entrance, I am guessing that you have cleared out enough of the tar babies to enter the chamber, so that your problem is getting to the tar mother. Here's what I did.
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×The problem is to find a place where all the tar babies will be in front of you.
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×Hang out in the area to the far west of the chamber.
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×After you have killed off the bulk of the tar babies, the tar mother doesn't spawn enough babies to keep you away from her.