I would stick with 19's. Since that is the case.... LM's are your best option. LMR's are not available in anything wider than 10" in 19's. That's too narrow. I would get LM's in 19x9.5 front, 19x11 rear.
'13 SSII M3 Coupe - KW Clubsport 3-way (Eibach Front Spring Conversion), Akrapovic Evolution, ESS Tune, StopTech Trophy, IND Euro Front Bumper and Gloss Black Mirror Covers, TMS Studs/Lugs, BMW Performance Carbon Fiber Spoiler/Interior Trim/Center Console, BMW Edition Grills/Gills, BMWPedals Extended DCT Paddles, Mode Carbon GT4 Splitter, Advan TC3 (18x9.5/10.5), BBS E05 (18x10/11), G-Force Rivals (275/35/18, 295/35/18)