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I only use AD08Rs on the street, which is why I have all those measurements above available. If you're looking to use AD08Rs then my measurements would be a good indication of likely section width but always double check. You should be around 283mm with an AD08R on an EC-7 18x9.5.
I'm guessing you'll be using the et58 offset. I used an effective et55 offset on an 18x10, which had a 288mm section width, so your inner clearance (with respect to the tyre) would increase by 0.5mm (practically the same), while the outside (guard/fender) clearance would increase by 5.5mm - you'll also have additional clearance to the wheel itself, i.e. 3.3mm inside and 9.4mm outside. You just need to make sure that you perform sufficient guard/fender lip modifications and consider ride height (raising if necessary) to allow fitment of a tyre that wide. If you needed additional clearance on the inside, and you still had ample clearance of the outside, then you could use a 3mm spacer. I don't like using spacers, especially on the track, but it can be a useful tool if it's difficult to come by custom offset wheels.
I also prefer the shorter 628mm OD tyres but have also run 635mm OD tyres (255/35/18 and 295/30/18) and 643mm OD tyres (265/35/18) without any issues. I don't think OD is an issue (at least not on my car) until it is around 650mm, which is when tyre section width needs to be decreased to ensure rubbing on the fuel filler tube doesn't occur.
Every car is different (mine took a lot of time, effort and money to fit), though, so take your baseline measurements and work from there.
The Michelin PS4S and (I presume an equivalent) Continental are Max performance tyres, whereas, I only use an Extreme performance tyre at a minimum on the road e.g. AD08R (I may look at the RE-71R next) - I would also run a Pilot Sport Cup 2 (or the A052 in 265/35/18 if I was in the US) on the street - there's no need for anything less where I live.
On the track, it's either semi-slick (R-comp) or full slick.
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