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If you are looking for a wider tire, thinking that it will have better grip, then you should consider that the compound is more important than the width with respect to grip.
If you want to stick with run flats, then I would stick with stock size so that the run flat sidewall lines up with the rim width.
The supercar tires that come on the Z51 have a spec of 220 which is a pretty soft tire. My 2c
I'm running BFG KDW2s in the sizes you want and am very happy with the improvement in the ride and handling of my car. However, the downside is that you could get stuck at the side of the road with a flat. If you use a can of "Inflate-a-flat" be prepared to replace your tire pressure sensor.