Gearbox Method for extra weekly gains: Consume 19 blue trophies to reach 11970 rep, and then consume a purple trophy to reach 13410/week.
Alternatively, as reader Aldalok suggests, you can use 21 Green + 10 Blue or 7 purple + 3 blue to get to 11970 rep.
You can go over the 12k weekly cap as long you use the last item <12k. The reputation gain over 12k are not lost.
Here is a handy chart you can use to see how much reputation and Gray Helix components you can gain.
So I can hit Champion next week if I can get a bunch of blues ready... We'll see.