Rokka no Yuusha
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Not quite the same setup, for one they dealt with the barrier, they can move which is why they don't have to find the traitor before progressing. So they can actually progress with their mission while having to watch out for the traitor instead it being all about catching the traitor.

Also if the second seasons begins with the first scene of book 2 (started reading today)
Spoiler: Novel 2 beginning spoiler
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Then it starts with a flash forward of someone admitting they are the seventh, I won't say who. Though I think they aren't actually the seventh