“It could be that women coincidentally smell my terrible BO when I mention I want a long-term patner, but I doubt it.”
It could also be that your signal of interest is the catalyst for them deciding to act on their pre-existing feelings of doubt. Perhaps they were already harbouring doubts but didn’t voice them until you, essentially, forced them to decide.
My anecdotal evidence is that, as you point out, a relationship formed on desperation covered up by acting tends to end the moment the acting dissolves. This implies that sustaining such relationships means acting for the rest of your life, an outcome you probably want to avoid.
Given that your criteria for a “success” are, essentially, “going on dates” and “having sex”, I’m not sure whether you’re content merely maximizing those two factors or actually care about the resulting relationships being fulfilling, but I’ll give you the benefit of the doubt and assume you’re actually interested in trying to maximize the latter.
As such, the actual advice I have on this topic is that rather than trying to act away your desperation, it’s both more effective and ultimately more rewarding to just “simply” decrease your level of desperation. A discussion of how to accomplish this would be even more out-of-scope, but in my case it essentially amounted to about a year of psychiatric treatment. The benefits of this are not just that it increases your life satisfaction in general (even while single), but also, importantly for this topic, allows you to shift your dating strategy away from “soliciting a large number of short-term dates in rapid-fire manner” and towards “randomly meeting people dynamically in environments sustained over longer periods of time”. I think that this is more successful and rewarding strategy in the long-term, and not one that depends on PHTG (nor where it would be beneficial).
In summary: The best way to play hard to get is to just… actually be hard to get, which implies being happy enough with yourself that you don’t really need a partner in your life; especially if they’re not helping you achieve your real goals. (Besides “having sex”, I mean. But then, why not simply pay somebody?)
Adding to this, basically every word can be used as a sexual euphemism, especially for genitalia. So it doesn’t surprise me at all that the centroid, which is sort of the average of all words, can be defined as such.