Yeah, those are touring tires.
If you want good "turn in", which is called transitional response, you'll want to get an ultra high performance tire. Look at what the SCCA autocross class STS guys are running. For the street, an inexpensive tire like the Falken Azenis rt615k is very sticky, has a VERY stiff sidewall and still has decent life. The bad part is that it's fairly noisy - but most ultra high performance tires are.
Post pics. People LOVE photos.