Motul has a 0w40 that is specifically recommended for the 370z. It's about $60 for a 5 liter jug... (5.1 quarts) Just enough for a complete oil change (if you don't have an oil cooler). I'm trying it this weekend. Motul makes all of Nissans oil. Including the super duper Estér Oil.
Motul 8100 Synthetic Motor Oil: JSC Speed