1. Use visual contrast early
Because every answer already belongs to Gintama, the only contrast left is inside the pool: 5 characters, all listed for 2006, where white hair appears on only 1 of them, while black covers 3. Two openers that share a hair colour spend a turn without splitting the board.
2. Let year split smaller pools
Genre is fixed here, so year and eyes carry the load: red eyes are the rarest tag at 1, and blue the most common at 2. Bracket the era first, then let the remaining visual clue choose between the survivors.
3. Memorize a few anchor characters
A small group of recognizable anchors is enough to carry most solves. For Gintama, useful anchors include Gintoki Sakata, Kagura, Kotaro Katsura, Shinpachi Shimura because they help you remember distinct clue combinations inside the current pool.