I am really feeling kind of snarky about this, so you might want to discount my opinion.
We spend so much of out limited energy fighting over naming conventions. Yes, I know that words matter, but at this point it seems this fight is form over substance. It also risks re-inventing the wheel in terms of research (which we all know is difficult anyway). If we endlessly subdivide PEM vs. PESE some researchers who are not familiar with our endless internecine infighting may actually get distracted from the central idea of worsening with exertion and figuring out why and how that happens.
I guess I think there is stigma against chronic illness full stop. At some level we need to fight that stigma more directly, rather than getting stuck on the name. It's distractor from the fear and distain for sick people. I also think that this disdain is faced by people with all chronic illnesses. All (whatever the diagnosis) of us are pegged as lazy, malingering, not wanting to do the work to get healthy (with the underlying false assumption that hard work is the case of health). That's what we need to attack. We have the opportunity to help not just ourselves, but all sick people. We are the poster children for this since we have PEM/PESE/whatever you want to call it. But all sick people are benefited by rest, real healthcare, and social justice. Let's focus on that, and not what really amounts to a spelling error.
End of rant.
Isn't there some Monty Python sketch about a rock band fighting over their name instead of making music? That's us.