Quote - @ cobaltdream,

Have a look at my second image on the previous page, the bottom part of the image. It's only an anti-aliased preview, not a render, but I think it shows that the convex toroid section shape looks quite realistic, especially the way it catches the light. It should do, because it is not far from the shape of a real iris. Compare it to the default dish shape, or convex sphere section from the previous image.

i wish we could quote images. ah well.

actually, your image shows that it shades much less well, imho.  that's part of why i'd be concerned with this as a more permanent fix (say new eye geometry).  you've got a photo texture with so many burned in effects, of course it looks more realistic without any additional shading.  you can see the reflection of the lashes in the texture, and the highlights are burned in as well.  that's great for lighting that's similar to what's burned in and fairly even (as yours is), but i personally find that kind of texture absolutely unusable in practice.  lots of people use textures like that very, very effectively, and many well-known and popular merchants sell them.  they just don't work very well for me.

yes, getting rid of the doubling of shadow is good.  i'm certainly not for making geometry or anything else double the effect of burned in lighting.   but with a proper texture that doesn't have lighting effects burned in, it wouldn't have most of the shading you're showing now nor the shading from the geometry.  i'd anticipate from the shading of the untextured model, it would just look painted on and weird to me.  but i could be totally off.

edited to add, imho, the untextured view also looks absolutely nothing like the inset diagrams i've seen of irises all over the Web (and at my optometrist's) , and certainly not like the opposing shading i saw on my own irises just a short while ago.  but to each their own, and i certainly applaud your efforts.