Hi Simon - I notice your curves are degree 2 - is that deliberate? For making smooth pebbly shapes like this, I would use degree 3 at least to get nice curvature continuity. NetworkSrf will override the curve continuity with degree 3 but still, I’d think you want smoother curves…At any rate though Network gets you something OK with the curves suggested by Eddi, - check carefully at the front and back - see how it gets a little out of hand there as it approaches the singularities?
For a shape like this, I’d try to force the singularity to the top by joining the base curves and splitting the verticals, then Network it.
-Pascal