Josh, good post. The thicker the wood the more work it should do to cut down on set. Therefore, a pyramid bow, which has thicker near handle wood should bend more there resulting in a circular tiller.
Also, as mikekeswick said, bows with parallel limb profile out to just before the tips should show an elliptical tiller and somewhat stiff the last 6-8 inches.
As DWS pointed out, sometimes you have to remove wood from the belly in a pyramid bow.
Jawge