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I have Toyo RA1 tires. 275/40/17 305/35/18 They will fit perfect. No problems at all. I even run 295/40/17 315/35/18 Kumho V710 for autocross. All on stock Z06 rims.
The Toyo RA1 when new are not that good. You feel like your driving on 4 flat tires. After about 25% worn out do they start to feel better. In fact the more they wear out the better I like them. Mine are just about to the cords and they are working great.
I have 6 track days on them and maybe 800 freeway miles.
Kumho MX tires work good from the get go and gradually get less traction through there life. For me about 3500 miles. The Toyo RA1 start out horrible then they gradually get better as they wear out. Much more traction then the MX tires by the end of it's life.