Well, Q2 should be enough for Advanced pace, but that will be pushing them.
You could go for a DOT tire, which will give you a lot more grip but might not last longer, and you will have to run tire warmers.
If you can have a spare set of wheels, the Pirelli Superbike Pro (slick with the redline) is a great option, it doesnt necessarily require warmers and it wears like iron.
If you do ride on the street and want a DOT most of them are comparable, i would go with what you can get trackside
Michelin Power One Cup
"The ZX-10R is capable of being perfectly docile and tractable, but few men are capable of resisting its ever-present voice urging them to just twist it and see what happens."