I can't imagine Republic is different from Empire in this regard (my Trooper is still just 41) but I completed all these with my BH long before the Black Hole was added and all pieces except the chest could be obtained through quests on Corellia. As a previous posters has stated, the chest is now available from The End of Torvix quest.
EDIT: I don't recall the name of the quest but I recall it was in the first area (for boots) but this would not help you as I am Imperial and you are Republic scum.