So if we tiller a non perfect pyramid to look like a perfect one, the bow is not correctly tillered.
You can't get the circular bend with constant limb thickness on a non-perfect pyramid, but you can if you tweak the thickness in the outer half of the limb. I don't know if that should be considered 'not correctly tillered' or not. The red oak lam bow I did with the lever tips was very close to circular tiller with the tips stiff, which to me is very close to an optimal arrangement of mass and strain. This is what Arvin keeps chasing and his bows have shown the results of those efforts.
I haven't found any need for more than the 2-3" parallel out of the fades, but I am sure the longer section you suggest will work fine if the thickness is tapered to suit.
In short, it's my strong opinion a pyramid bow shouldn't actually be a pyramid, nor tillered like one. It should start out parallel, then straight taper to stiff tips.
Well, that certainly isn't a pyramid bow as you describe. It's basically an ASL and will need thickness taper and tiller to suit.
Mark