How do I get high SHGC windows approved using 2012 building code?

I have a building plan which has a roof overhang sized to completely exclude south side summer sun on the upper story, and a balcony which completely shades the lower story in the summer.  I want to use SHGC .66 windows on the south side to admit as much winter heat as possible, but I'm running into trouble with the building inspector.  He approved my permit  (which included a complete window schedule) and then said that I'd need to have windows that pass ResCheck.  ResCheck merely averages the SHGC of all the windows, and since I have hardly any square footage of non-south facing windows, I don't meet the requirement.  There's an option for adjusting the effective SHGC based on the overhang projection, but they don't differentiate among south, west, and east facing windows, so the credit is not really relevant to my application.  Has anyone on here had to face this problem and how did you solve it? I have not broken ground yet so I still have a lot of flexibility. Thanks!

I haven't had to jump through any such hoops (here the building inspector is happy if your plans are better than a napkin sketch), but I just had to comment that not differentiating between south overhangs and others is insanity! I sure hope more recent versions of the code are more intelligent with regard to actual solar effectiveness, and that your area adopts them soon.