That's a really beautiful shape, N-drju. And as KlausK shows it should render just fine.
The edges that you are seeing in the Blender 3D window and in your TG rendering are caused by using too many polys. I know this sounds counterintuitive. But when you subdivide your model so early in the process, any small rounding error in subsequent warps and transforms may prevent some of those tiny polys from deforming smoothly. And once they're out of kilter it's impossible to fix them. It's much better to start with as few polys as possible, apply a subdivision modifier, then adjust the cage to achieve the shape you want. Then, when you're happy with it, bake the subdivisions.
IMHO the main shell in this object has many more polys than you need. Probably 10-12K would be fine. I know this isn't a Blender forum but I'd be happy to share an example file if you are interested.