Just a reminder to any that don't yet realize it...
When you claim a T6 Reputation, it 'upgrades' all of your reputation traits to a Rank 2 variant. The game does this by removing the old trait from your available list and replacing it with an upgraded T2 version.
When this happens, the trait is unslotted as it no longer exists, but the replacement trait does not equip automatically.
This means that if you go through in one shot and claim T6 on all 12 reputations then every trait that is not Personal Ground, Personal Space, or a Starship Trait will be unslotted leaving you with no traits selected.
Don't forget after claiming your T6 Reputations to re-slot all your traits.
If you don't remember what traits you use, make note of them before claiming T6. The trait is only replaced after you run the 5 mark project to Claim T6. You have until that time to make note of your current traits.