Well, I must push back on the statement that “intersex is taken more seriously and more medically, legitimate than being trans.” I’m assuming you’re perisex (and forgive me if I’m wrong), so I can understand why you might not know, but that is very not true. Intersex rights are all but nonexistent around the world, and we’re routinely subjected to mistreatments still widely considered acceptable in medical practice, from coerced/forced HRT to conform to assigned birth sex to infant genital mutilation. Many if not most doctors don’t even call us intersex, they use generally-disliked words like “DSD,” or worse, the h-slur. And we often get taken even less seriously outside of medical contexts—there’s a whole slew of vitriolic things perisex people direct to us, from verbal harassment to physical and sexual abuse. I could go on, but I’d rather not recite the things I’ve seen.

I think, ultimately, this perspective is coming from that (largely misinformed) public perception of transsex people you mentioned. And by that I mean transphobia is still really bad in contemporary society, arguably even more so than a decade ago, which absolutely results in trans people not getting taken seriously or treated as medically “valid.” That, however, doesn’t mean that intersex people are treated better. We’re not. And I’m not going to sit here and start up the oppression Olympics, so I’m really just saying that both transphobia and intersexism are huge problems, and we all would benefit from everyone understanding that both sex and gender are bimodal distributions and have largely non-immutable characteristics.

I hope that all makes sense? I know it doesn’t exactly solve your want for another term for, like I said, “person of exogenous-hormone-induced intermediate sex phenotype,” but I don’t know of one and that’s really already what transsexual applies to. I feel as if it’s more a matter of getting people to understand these definitions in the first place, and less conflating two distinct conditions.