I played that game some more. The pirates did eventually return to a more passive mode, although they are not quite as passive as they were - they have tried to enter my territory and sever the "roads" a few times, and 3 or 4 ships have attacked the star systems (nothing like the 10 to 20 that were attacking each turn during the frenzy, or would have been if I hadn't been thinning out the invasion ships by attacking them before they could attack so as to reduce the collateral damage). I think what triggered the end of the frenzy was them advancing to the second era, although around that same time they captured two systems from the Avowers including their capital. Via bomber recon I can see that they took a system from the Red Syndicate. I knew who it was based on the name, but a while later a Syndicate battleship wandered over close enough to get contact before the horde destroyed it. The Forge likewise made contact a while after that (also just before the exploring battleship was destroyed by repeated attacks from pirate delta destroyers). Halis also wandered by and I didn't see their battleship get destroyed, although I have to assume that it was destroyed not too many turns later.
I'm not sure how, but the Avowers have colonized at least one more system (the only 7 planet system I have seen in this game - it's quite nice and could support a working population of something around 32 if all the extra population buildings were to be built everywhere they can be) and also went and retook their original capital, probably only about 10 or 12 turns after the pirates got it.
After the pirates calmed down from their suicidal frenzy I built a starbase about half way to the closest star system and then started a colony there (not a great system, but it is only 7 tiles away and does have a health resource on a planet in the 3rd influence zone - grain, I think). I have built a second starbase on top of an asteroid field with oil in it, and built the extraction facility and connected it to my trade network, and am about to launch a fleet to colonize another star system, off on the other side of the oil by several tiles, that has more population potential then my first colony and has wine in the second influence range. Currently it is, I think, just a little after turn 275. The turns do tend to fly by most of the time because frequently all there is to do is a little recon and a couple of attacks with squadrons, which goes pretty quick.
I have to admit that this game is strangely enjoyable. Probably at least partially due to not having expected anybody to have survived this long. Currently it looks like the Brotherhood is the only civ that has been completely wiped out. The Avowers and Syndicate are managing to stay about 2 to 3 techs ahead of me so far, I think this is largely because they appear to be trading techs with each other, but I have nobody to trade with (I have no techs they don't, and the Forge and Halis have no techs I don't, unless one of the other two have recently given them some techs for some too small amount of money).