You were doing good until you set the limit at $200 per tire. The gold standard autocross tire is the Bridgestone RE71R. It's the highest grip 200 tread wear you can buy but you're looking in the $260-$300 per tire range.
There are some people I know that are running the Nexen N FERA SUR4 and while it's not quite at the level of the RE71R it appears to do a decent job. It's definitely in your price range.
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