If you want to keep factory size and have improved grip with front and rear matching tires (same brand, same tread design) then it appears that Michelin SS are the best choice.
Toyo R888 come in the 285/35/20 but do not offer a 19 inch version that will work.
Hankook vents rs-3 (stick track tire) comes in factory rear size but the 19 is .7" shorter than factory.
If you absolutely want to stick with the factory wheels I would go With the Michelin's.
One of the 13 owners (cool cobra) got new wheels and with with toyo r888 with 315/30/20 in the rear and 285/35/20. These are perfectly matched and have the exact same ride height (27.6). CaR would lose some of the rake vs stock. Granted he has wheels that will accommodate these tire sizes.
It comes down to what you want (traction, looks, weight, performance, ride quality).
18's better performance, weight, ride, tires with traction are available
19's good compromise but tire availability stinks.
20's looks, solid tire options but gives up some ride quality, weight and performance.
Better grip? I'd have to say the Nittos. BUT if you want to compare more like tires, I'd compare the Michelin SS's to Nitto Invos. The Invos are made for water and last longer. HOWEVER, the Nittos also have only a "W" speed rating (168 MPH) and therefore have a lot more sidewall flex than the Michelin SS's do. If you are only driving it on the street and want really good traction, I love my Nitto Invo's. But, the tires handled like crap on the racetrack when I had them on my 2008 Corvette Coupe.
The Michelin is the all around better tire. But for the money, the Nitto probably can't be beat.