I like the duel idea, and how you set it up. One thought for your consideration, as an alternative option for both duels and directors:
The director is elected, and his/her power is to choose between a traditional lynch (top voted dies) or a duel (two top candidates duel each other). Whoever wins the duel might be based on their strength, but perhaps also on some other mechanic... rock/paper/scissors is one idea, but I'm assuming you already read about and considered that. Having it based on strength might be revealing... and it might not be. Having it based on both strength and chance might be interesting. I like the idea of duels, but I also like the idea of there being traditional lynches if the Director wishes so. This is a rough sketch of an idea... you can play with it or toss it out.
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