Here's a pic I took a few years back of a 265/35-18 R1 next to a 275/35-18 NT-01, both on 9.5" wheels. The 265 R1 was about equal to the section width of the 275 NT-01 when measured; however, the R1 sidewall to tread face profile is different from most all other tires out there. Note how it carries its section width out to the tread face while most tires have some curvature from maximum section width to the tread face.
I've used 275/35-18 R1s also (E39 M5), but they created some clearance issues where no other 275 R-comp I've used on that car ever did (Hoosier A6, NT-01).
Just an FYI post...sounds like the 275 R1 will clear ok on the M3.
2011.5 M3 sedan 6MT, Silverstone, slicktop, loaded
2001 M5 LeMans Blue/Silverstone
2006 330i 6MT Red/black, ZSP, Nav, etc
2007 328i wagon Silver/gray