Gender is not "for blurred lines", it's about social constructs, and society happens to be a complex emergent system, so its binaries tend to be approximative at best. The point of separating it was not to deal with blurred lines, but to deal with sociology in an unequivocal manner.

Sex is about biology which is also a complex emergent system. You may assert that sex is binary and immutable in the whole field of biology, and I don't know what your credentials are to support this claim but my sources beg to differ. I've read and heard biologists use different definitions for different subfields and contexts, and argue that none is a simple binary when you start to look at individual expressions. Even your article starts with three qualifiers for sex: "anatomical gonadic and chromosomal", and deals specifically with people who may have none or both gametes. So much for the major scientific win of an immutable binary.
You seem to be decided on one definition having the primacy over the others and I get why: gamete size is basically the first logical step of the male/female differenciation in species, so it makes sense when your study is about reproductive strategies across species and how sexual differenciation is so widespread. I'm not sure it's going to make as much sense when your field of study is embryo morphogenesis or ethology, though.
All the biologists I've met or read are actually fairly used to "sex" meaning different things in different contexts, and they're absolutely going to be fine with people calling themselves intersex if they don't want their biological singularity defined by a disorder.

Also, did you read the part in your own article where they said the nomenclature "DSD" was decided in Chicago when a bunch of doctors thought maybe "hermaphrodite" and "intersex" was maybe pejorative? It's okay to just ask the people who actually have it what they prefer and use that, it's just phonemes, it's fine. No scientific content is removed by being considerate.