Reviving an old thread. I have just replaced a Michelin Cross Climate 2 rear tyre. It has been excellent for wear and grip in my opinion. It has done almost 7,000 miles and still had 3.5mm of tread left, better than normal. Normally I would have left it for some more miles but I have a long trip around Europe coming up and thought it may be cutting it a bit fine. The only down side of the Cross Climate 2 has been the sidewall "bulge". I have measured this with a bit more accuracy than before and it measures 187mm max. at 28psi and unloaded.
My earlier measurement of the Goodyear Vector 4 Season must have been a bit optimistic as the sidewall scuffing of the Cross Climate was fairly minimal, whereas the Goodyear was significant. My laser rear wheel alignment is spot on, now I know where the target point is for good alignment. Having previously fitted a Bridgestone A005, that performed well and was "slim", I have gone with another one of those. Sidewall max bulge is 180mm with that and it gives a generous 6mm clearance with the drive belt when all nicely aligned. It gets top marks for wet weather performance, a major consideration for a M3W. I would say it has much the same performance as the Cross Climate, possibly a slightly higher wear rate?
If you have an early car with no outer retaining ring on the rear sprocket then the belt clearance will be fine with most tyres and you could even use a spacer on the rear sprocket, although the front sprocket may have the belt running hard against the retainer. That is another problem to balance though. Not all 175/65-15 tyres are the same size.