The surgery begun tonight by shaving and filing flat the two upper "corners" of the nose piece. The flat surfaces will hopefully provide a solid base to build the new volumes on.
With regard to lamination or epoxy putty - thanks for these tips. I haven't really tried any of these yet, so I'm sticking with a method which is familiar to me, using sutiable scrap pieces of plastic bonded with thick superglue. Gap-filling superglue has a significant advantage as filler. When dry, it is in all respects similar to stryrene - no risk for shrinkage, softness, chipping edges. Hardened superglue can be sanded and scribed consistently with the surrounding plastic.
In this case, "a suitable scrap piece of plastic" is 1/144 fuselage half of a Tornado which is lending its nose cone to this project.
Here's everything bonded with generous blobs of Zap-A-Gap. Looking good...
A bit of preliminary sanding finishes the job for today.
I feel that I'd need to proceed very carefully from this point forward. Attached spinner servers as a visual guide, but I'm feeling that I'd need more aids to ensure a symmetrical shape.