Unfortunately, this does not seem to quite do the trick for me. I still see overlapping triangles in the regions with high curvature.

Yes, that's correct. It requires either depth or stencil tricks to prevent drawing to the same pixel twice, or much more involved, correct computation on the CPU. If you turn on depth testing below, you'll see that it at least prevents drawing twice.

(Please read nothing into marking this "resolved"! I appreciate the feedback! I still haven't quite figured out how to work around unresolved comments without them seeming rather in the way!)