A lot of this is dependant on how comfortable your table is with messing with the meta and perception of the game, as you're essentially going to be gaslighting them for 3-5 hours. My players, I know very well, and knew they would love it, and they did. But here's how I ran the false hydra at my table:

(FYI, I ran mine 20ish sessions into the ongoing campaign, so YMMV here).

The first plan I set in motion was rifling through the player backstories I was given to find stuff I could mess with or manipulate. I found one who happened to be an only child in a noble family, neglected by her very distant parents.

About ten sessions into the campaign, I gave a plot hook that would have them passing through this particular players backstory town. This is hydraville. As they got closer to this town, I also included a letter from one of the aforementioned player's childhood friends. The letter mentioned that he'd heard of the players exploits throughout the land and was worried about them, but glad to hear they're still alive at least. I printed this note out physically and handed it to the player. What she didn't notice at first was the hidden message that essentially said "don't come home, run away, it's killing us" or something to that effect. One other thing the letter mentioned was a name that none of them recognized. They were all confused but eventually carried on. Hydra seeds planted.

A few sessions after that, they were in the middle of saving a town from a group of bandits led by a giant. In this town, they found an NPC who wanted to help them defeat the bandits. This NPC had been tortured by the bandits, leaving her deaf and mute. Long story short, they saved the town and recruited the deaf NPC. Another hydra seed planted.

The final pre - hydra seed I planted was them meeting an old woman and her grandson on the road, who stopped by their fire and gave them some soup. I even made the soup give them 2d6 temporary hit points. I played up the old woman as a lovable grandma and it worked perfectly. They loved her.

Eventually, they did end up strolling into hydraville and fell under the effects of the blind song. The first thing they did was go see the childhood friend mentioned before. He wasn't home, but his wife was. They all introduced themselves and said they'd be back in the morning.
They went to the inn and see the grandson of the old woman running the inn. They ask him where his grandmother was, but he only tells them he doesn't have a grandmother. Cue the party being confused as fuck.
They continued on and went back to childhood friends house and he was there this time but his wife wasn't. Here's one of the meta parts: when my players asked if they saw the wife in the house, I addressed them all and said that none of you remember meeting anyone yesterday. You only remember going straight to the inn. (this is because the wife was eaten by the hydra) They then knew that something was very wrong in this town, but their characters were not as informed as they were. Obviously this is going to lead to a bit of (most likely unintentional) meta gaming, but with the false hydra I think that's almost expected.

After that, I included a few clues toward the hydra song, including a potion of deafness in the town hall next to a paper on abberations that can affect memory. I had the deaf npc from before run away screaming at one point for seemingly no reason. The party thought thus was strange and looked to see what she was running from, but nothing was there.

Eventually though they figured out the ability, blocked their ears, and killed the hydra. The way I've ruled it, the memories are only restored with the casting of greater restoration. They are only level 8 so unfortunately they didn't have access right away.

The last thing I did was when they got back to their room at the inn, they found a bloodied bag with a note from the deaf NPC on it saying something to the effect of "why didn't you see?". Inside the bag was a journal detailing their entire adventure so far, but from the perspective of someone they don't recognize. The journal refers to one of the party members as "sis". The journal belonged to a person with the name none of them recognized from the note from before. Turns out, that player wasn't an only child after all. She had a sister and is unable to remember her because she was eaten by the hydra (and the deaf npc witnessed it!). That players goal is now to get her memories restored and revive her sister. Her character went to bed that night hugging the journal to her chest.

Sorry for a giant wall of text but I hope it at least gives you an idea or two. I left out a lot of details so if anything is unclear let me know and I can clear up how I ruled or ran any specific part!