Get close to other strands sytems (say 1 jump away) and start attacking renegades. If a strand ship comes it ought to just attack the renegade instead of you. After the renegade is destroyed jump out immediately because the strands ship'll attack you if you stay. Repeat a few dozen times, and it might help.
Another thing to do would be to bribe your way in to var. strand planets and frequent their bars. Sooner or later a government official will come up to you and offer you a mission (fight renegades, deliver emergency supplies, etc.) and after completing the mission your karma should have increased (possibly, repeat if it didn't do that).
Also, the Zidagar are the best! Why would you want to change?
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Diddly,
"Well, we could grind
our enemies into powder, but gosh, we did that yesterday."