Lots of things going on there!
I'll tell you what I see there without trying to translate it to English. First of all there's a bump in my understanding because some
perífrasis verbales are mixed there with other verbs. "Querer hacerlo" is appart, but "poder hacerlo" is a
perífrasis, that's why you can say "pueden irse" or "se pueden ir", but you can only say "quieren irse". However, people massively say "se quieren ir" ("they love each other go") with the meaning of "quieren irse" (they want to leave). That being said, I instantly choose "quisiera haberlo hecho" -though "querría ..." is OK by me- but never "pudiera haberlo hecho" with the meaning of "podría haberlo hecho", so, are there two meanings there? Well, yes, at least for me:
pudiera haberlo hecho ---> calls for probability, the same way as might-may-could-can (or might-could-may-can) ---> it's sort of a might, or better, the start of that scale.
podría haberlo hecho ---> calls for hypothetical alternative events in the past ---> I would have been able to do so, but I didn't
The tip of the iceberg, so far. Let's go on further. I read "podría haberlo hecho", "hubiera podido hacerlo" and "habría podido hacerlo" and they are "similar" yet strangely different. The first problem is first and third person being the same conjugation as "pudiera haberlo hecho" calls for probability when a he or she is involved; the rest is pretty much like this:
hubiera podido hacerlo (yo) ---> de haberlo querido, hubiera podido hacerlo, pero no lo hice (I had the potential to do it, but I chose not) --> subjunctive calls for "probability", or better said, for 50-50 events, or 80-20, or whatever implying multiple outputs, or even better put, for split realities.
habría podido hacerlo (él o ella) ---> como estaba la puerta con llave, no pudo entrar; de no estarlo, habría podido hacerlo (Some different circumstances could have freed the potential for him to do it)
podría haberlo hecho (yo, él o ella) ---> de haberlo querido, podría haber roto la puerta, porque estaba cerrada con llave, pero no hubiera podido hacerlo legalmente ---> it's sort of a wildcard expression, but it breaks the
perífrasis verbal, keeping its association with potential but losing its association with permission (note how I had to go back to the other form to express that)
Ok, this is quite a lot, and we've only skimmed the surface of it. Remember that Spanish has no modal verbs ... until the ghosts of modal verbs show in Spanish

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There's more to say on your question, but let's leave it to follow-up posts in this thread.