By far the best way I’ve found to use the false Hydra so far is a week or two ahead of a session, to send out a link about the false Hydra to your group and be like “look at this neat monster I found!” Then present them with a story about people disappearing from a village and watch them invent their own false Hydra.
If you wanna de-metagame the same idea, share it in world as folklore then ‘break character’ to gush about it.
If the players dig deep enough about the false hydra they ‘discover’ they’d find it’s a rumour spread by the person who also spread the folklore in world, perhaps they’re a serial killer or supporting some form of underground railroad or something.
The only thing this doesn’t fix is the root issue of “if you know there are people disappearing, then it’s not a false hydra”.