I'm guessing that you are using the current educational version, which means I can't open your model, being stuck on 2010. If you don't get an answer from someone else, I may be able to help from screen dumps showing your issue. Winging it completely, I would guess that your intuition is correct, that you need to break the single surface up into multiple surfaces. It is often easier for SolidWorks if you separate the high curvature regions from the low curvature regions.
Do the camaro tutorial