If all you need is the rep, here's how you cap it without even running the FP.
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1. Get a character to level 50.
2. Go to the Fleet > Mission Departures Elevator > Starfighter Launch Deck;
3. Grab the intro mission to Kuat, watch the cutscenes;
4. Go inside the FP through the door that should be purple since you got the mission;
5. Talk to the first NPC inside the FP, it will finish the mission and give you a purple reputation item.
6. Do this a couple of times on other characters and you'll get to Legend in no time.
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This was possible for me because I have many characters, but I understand it might not be so easy if you don't have many alts. And the purple rep item gives a lot of rep, especially if you got a rep boost on. Anyway, just trying to help out.