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.
The double fake
Tricking the players into genociding a village because a NPC has dementia
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".
I've found that in general it doesn't matter. If the party gets in their head that it's a False Hydra, then they will typically ignore or justify the discrepancy.
Slow down there, Satan.
For those of you who haven't already read the goblin punch blog post (which is linked in this post but is easy to miss), I strongly urge you to read it. It's a bit long but it explores the concept of this horrifying monster in a really interesting way.
As for actually running a false hydra... I dunno. It would be amazing if you could pull it off, but I think it would be a lot of work to set up if you're trying to manage real-life player memories as well as character ones.
I often find that blog post, which I thought was it's origin, reads too much like a creepypasta for me to enjoy.
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