There are at least three aspects of the current pirates that might seem dubious:
-the pirate base is a fortress surrounded by gauss guns
-the pirates mount destructive terror raids relying on numbers not stealth, and do nothing in between raids
-trade ports are an effective early counter since the pirates spend time chasing the trade ships
It might be more piratical to have a base that was defended being being difficult to approach- perhaps a nebula that prevented the use of squadrons and an asteroid belt that the pirate ships were immune to. Also, the pirate ships could use some kind of cloak or disguise. They should be able to capture ships rather than be forced to destroy them- if trade ships were instead captured and refitted as pirate warships, there would be a drawback to using trade ports as a defence. Pirates used to frighten trade ships into surrender rather than fight, it was the point of the black flag and the poor personal health care.
More than this, it might be an improvement to have the pirates linked more closely to the militias around independent planets, and to have a use for the ships that build up around the pirate base. Perhaps the surplus ships could be sent to restock or supplement the militia and the pirates lurking near neutral extractors? Once the neutral extractors bug is fixed and they are made noticeable to the AI, they might then have to be guarded after the initial capture.
A new pirate-only sub-cap ship or command cruiser might help, as the pirates lack subversion and sabotage abilities as well as stealth. Or these abilities could be added to the existing pirate ships. The pirate base might act as a rebel broadcaster, as well....