All of the quests associated with the Murder on Eridanos DLC on give between 1% and 3% Positive Reputation, which makes it impossible to complete it with a total reputation above 20% for SLUG or Rizzo's.
When I speak with Adjutant Sophia on The Unreliable after planting a corrupted tracking signal on Phineas Welles' computer my negative reputation with The Board does not decrease.