What makes you think that such a group can usefully be identified? (And from what I have seen hEDS is defined in all sorts of other ways - including symptoms).
I have run a hypermobility clinic and seen scores of patients. In my general rheumatology clinic I have seen thousands. Have you? I also know that the physicians who claim these things talk and write fairy tales. Each one makes slightly different stuff up, showing that none of them are actually talking about a single reality.
What makes me think that people with the same or similar features are more likely to have the same or similar underlying genetic issues? What kind of ridiculous question is that?
As stated earlier, there are obviously many issues with definitions, and with mixing traits with features/signs/symptoms but the way you portray this specifically makes me think you are heavily biased. It's just not completely random or arbitrary and hence potentially useful. It might not be.
Whether or not you have seen thousands of hypermobile patients, how does that relate to the logic behind subgrouping them in principle? I don't care much about your issues with your former colleagues tbh, these are just random misgivings to me, you either can explain what is you think they do wrong in more detail or it's just a waste of time to even discuss it.
I have spoken to hundreds of people with hEDS, read and seen thousands of comments, and reviewed most of the literature. This is similar to how you define your ME/CFS expertise, if I remember correctly. You have never seen or treated ME/CFS patients, right? I have hEDS, and I am interested in understanding the complex genetic underpinnings of this.
Please explain how you would approach this if not in the way it is currently done via hEDS. Genuinely interested. I doubt you will come up with a better idea, especially given the current constraints. In such a scenario, there will always be pros and cons to looking at specific families versus population-size cohorts. Both approaches are needed, and to get sizeable cohorts you need certain definitions that will always be somewhat arbitrary. It's absolutely obvious to everyone involved that this is not a monogenic (in the one gene for the cohort sense mostly) issue and polygenic in a complex fashion, that doesn't mean there is no overlap and/or useful signal. And while it can be, it's not automatically a mistake to mix traits with symptoms for definitions. There are trade-offs for everything.
By the way, what is PEM? You think that’s not a “symptom”? The entire definition of ME/CFS is based on it! The whole of ME/CFS is basically nothing but symptoms/features currently and you advocated (rightly so) for a GWAS!
Here are the criteria:
The Ehlers Danlos Society
https://share.google/MUl3XFvXhBKf0WOS
Not that many symptoms, right? Maybe 'random' traits and features, but not that many symptoms. One thing you are definitely doing is conflating bad research based on unproven causality re symptoms using diagnostic criteria with the diagnostic criteria themselves and it will be very difficult for you to argue otherwise. Based on what you have said here I doubt you have even read the criteria.
(I will not be back online for a while.)