Determined that shape must make a difference, I mulled over the
roof styles further, and I'm very intrigued with this one:

Here are my reasons:
Simplicity
The entire roof is a single face, which will make construction simple and inexpensive, maintenance rare, and runoff very manageable.
The Sun
This design favors one large wall over the other three, just as the sun shines from one cardinal direction more than the other three. This coincidence could be used to maximize solar gain, while minimizing cold and breezy north facing surfaces. By filling the large side with windows, the sloping eaves would welcome all of the winter sun while shading the home from the summer sun.
Large outer wallTypical roofs leave the greatest height in the house along the middle. This roof puts that height along an outer wall allowing the height to be used by dramatic windows (like mentioned above.) Ceiling height is only really impressive when it is drawn attention to.
Yes, all this attention on one wall does leave its short counterpart without much to offer, but certain rooms don't require tall ceilings, hot sunlight and good views, like bathrooms and storage
What do you think? No, it's not much to look at yet, but remember we are still just theorizing.