You can use a Pilot Road 2 or BT-021 on the track. Unless you're faster than mid-pack intermediate group it won't be the tires holding you back. The Power Road 2 has the same compound as the standard Pilot Power on the sides, so traction won't be an issue.
But if you insist on using sport tires, the stickiest are probably the BT002RS. The Pilot Power is a great tire and is plenty sticky for trackdays too. The Dunlop Qualifier is another sticky tire that can easily handle track duty. If you wreck on any of them it's not because of the tires...
<RANT>The Pilot Power 2CT is a bad, expensive joke. The softer edge only extends 1/2 - 3/4 inch from the edge of the tire, making it virtually useless for street riding, and it gets greasy/slippery with prolonged pushing from track riding.</RANT>
Something to bear in mind is that most track day orgs won't let you run tires that obviously have a lot of miles on them, so unless they are pretty new they won't let you out on track with street tires anyway.
Another thing to bear in mind is that proper suspension tuning will allow a dork on ST tires to pass you all day long even if you're on supersoft compound race tires.